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HTTP/1.1 200 OKConnection: keep-aliveContent-Length: 106978Server: GitHub.comContent-Type: text/html; charsetutf-8permissions-policy: interest-cohort()Last-Modified: Wed, 12 Dec 2018 13:17:52 GMTAccess-Control-Allow-Origin: *ETag: 5c110a80-1a1e2expires: Fri, 12 Jul 2024 02:35:03 GMTCache-Control: max-age600x-hosts-log-append: pages_hosts_ips:x-proxy-cache: MISSX-GitHub-Request-Id: 2246:37D38:1EDD950:1FAE38E:669093FEAccept-Ranges: bytesAge: 0Date: Fri, 12 Jul 2024 02:25:03 GMTVia: 1.1 varnishX-Served-By: cache-bfi-krnt7300058-BFIX-Cache: MISSX-Cache-Hits: 0X-Timer: S1720751103.228959,VS0,VE76Vary: Accept-EncodingX-Fastly-Request-ID: a47ef3fda3693a4f544208b7f0f45d7d9843218e !DOCTYPE html>html>head> meta charsetutf-8> meta http-equivX-UA-Compatible contentIEedge> meta nameviewport contentwidthdevice-width initial-scale1> meta namedescription contentUseless math is useful math. It can be used to generate more useless math.> meta nameauthor content> title>Francisco Blanco-Silva/title> !-- Bootstrap core CSS --> link href/css/bootstrap.css relstylesheet> !-- Bootstrap theme --> link href/css/bootstrap-theme.css relstylesheet> !-- Custom styles for this template --> link href/css/blog.css relstylesheet> link relstylesheet href/css/pygments.css> !-- Begin Jekyll SEO tag v2.5.0 -->title>Francisco Blanco-Silva | Useless math is useful math. It can be used to generate more useless math./title>meta namegenerator contentJekyll v3.7.4 />meta propertyog:title contentFrancisco Blanco-Silva />meta propertyog:locale contenten_US />meta namedescription contentUseless math is useful math. It can be used to generate more useless math. />meta propertyog:description contentUseless math is useful math. It can be used to generate more useless math. />link relcanonical hrefhttp://blancosilva.github.io/ />meta propertyog:url contenthttp://blancosilva.github.io/ />meta propertyog:site_name contentFrancisco Blanco-Silva />script typeapplication/ld+json>{@type:WebSite,url:http://blancosilva.github.io/,headline:Francisco Blanco-Silva,name:Francisco Blanco-Silva,description:Useless math is useful math. It can be used to generate more useless math.,@context:http://schema.org}/script>!-- End Jekyll SEO tag -->/head>body roledocument> nav classnavbar navbar-inverse navbar-fixed-top rolenavigation> div classcontainer> div classnavbar-header> a classnavbar-brand href#> img altBrand srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:25px;> /a> button typebutton classnavbar-toggle collapsed data-togglecollapse data-target#navbar aria-expandedfalse aria-controlsnavbar> span classsr-only>Toggle navigation/span> span classicon-bar>/span> span classicon-bar>/span> span classicon-bar>/span> /button> a classnavbar-brand href/>Francisco Blanco-Silva/a> /div> div idnavbar classnavbar-collapse collapse> ul classnav navbar-nav> li classactive>a href/>Home/a>/li> li>a classpage-link href/about/>About me/a>/li> li>a classpage-link href/books/>Books/a>/li> li>a classpage-link href/presentations.html>Presentations/a>/li> /ul> ul classnav navbar-nav navbar-right> li classdropdown> a href/ classdropdown-toggle data-toggledropdown>Teaching span classcaret>/span>/a> ul classdropdown-menu rolemenu> li classdropdown-header>Current | Most recent classes/li> li>a href/course/2018/08/22/math-122-fall-2018.html>MA122—Fall 2018/a>/li> li>a href/course/2018/08/13/ma300-fall-2018.html>MA300—Fall 2018/a>/li> li>a href/course/2018/08/13/ma242-fall-2018.html>MA242—Fall 2018/a>/li> li>a href/course/2018/01/15/ma241-spring-2018.html>MA241—Spring 2018/a>/li> li>a href/course/2017/08/22/ma524-fall-2017.html>MA524—Fall 2017/a>/li> li>a href/course/2016/08/12/math-141-fall-2016.html>MA141—Fall 2016/a>/li> li>a href/course/2016/08/10/ma142-fall-2016.html>MA142—Fall 2016/a>/li> li classdivider>/li> li classdropdown-header>Forums for Homework and Review Exams/li> li>a href/forum/2018/12/07/MA242Fa18RT.html>MATH 242 Fall 2018 Review Exams/a>/li> li>a href/forum/2018/11/26/MA300a16.html>MATH 300 Fall 2018 Problems from Chapter 11/a>/li> li>a href/forum/2018/11/17/MA122L13.html>Answers to Assigned Problems in Lesson 13/a>/li> li>a href/forum/2018/11/17/MA122L14.html>Answers to Assigned Problems in Lesson 14/a>/li> li>a href/forum/2018/10/30/MA242ga.html>Answers to Problems in the Notes of Geometric Applications/a>/li> li>a href/forum/2017/12/06/MA122Fa17RT.html>MATH 122 Fall 2017 Review Exam/a>/li> li>a href/forum/2017/09/06/MA524ch5.html>MATH 524 Fall 2017 Chapter 5/a>/li> li>a href/forum/2017/04/26/MA241Sp17RT.html>MATH 241 Spring 2017 Review Exam/a>/li> li>a href/forum/2015/10/23/integration-review.html>Integration Review/a>/li> li>a href/forum/2014/12/01/MA141Fa16RT.html>MATH 141 Fall 2016 Review Exam/a>/li> li>a href/forum/2014/12/01/MA142Fa16RT.html>MATH 142 Fall 2016 Review Exam/a>/li> li classdivider>/li> li classdropdown-header>Selected Class Material/li> li>a href/teaching/2014/11/08/past-classes.html>Past Sections of Undergraduate Calculus/a>/li> li>a href/teaching/2014/11/08/Mathematical-Imaging.html>Mathematical Imaging/a>/li> li>a href/teaching/2010/10/27/an-introduction-to-algebraic-topology.html>An Introduction to Algebraic Topology/a>/li> li>a href/teaching/2010/09/24/distributions.html>Introduction to the Theory of Distributions/a>/li> li>a href/teaching/2010/07/09/ma598r.html>MA598R—Summer 2007/a>/li> /ul> /li> !-- dropdown --> /ul> /div>!--/.nav-collapse --> /div>/nav> div classpage-content> div classwrapper> br />br />br />br />div classcontainer theme-showcase rolemain stylefont-family: Helvetica;> div classrow> div classcol-sm-8 col-lg-8> p classentry-date date published> time datetime2016-09-10 itempropdatePublished>September 10, 2016/time> /p> div classmedia> a classmedia-left href/post/2016/09/10/periodic-table.html> img srchttp://blancosilva.github.io/images/hydrogen.png stylewidth:200px;> /a> div classmedia-body> a href/post/2016/09/10/periodic-table.html> h4 classmedia-heading>How accurate is K-means clustering as predictor of subcategories in the metal-metalloid-nonmetal trend?/h4> /a> I started with a database containing some of the properties of the chemical elements: Atomic number, atomic weight, electronegativity, ionization potential, atomic radius, atomic volume, boiling point, covalent radius, density, heat of fusion, heat of vaporization, melting point, and specific heat capacity. A quick... div styletext-align:right; width:100%;> a href/post/2016/09/10/periodic-table.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2016-09-04 itempropdatePublished>September 04, 2016/time> /p> div classmedia> a classmedia-left href/post/2016/09/04/bokeh-dijkstra.html> img srchttp://blancosilva.github.io/images/bokeh-dijkstra.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2016/09/04/bokeh-dijkstra.html> h4 classmedia-heading>Interactive Shortest-distance calculations on Triangulations/h4> /a> As a means to bring attention to my latest book, Mastering SciPy, I wrote a blog post summarizing some of the techniques illustrated in one of its chapters: Computational Geometry in Python. On that post, I created an example of computation of shortest distances between two vertices of the constrained conforming De... div styletext-align:right; width:100%;> a href/post/2016/09/04/bokeh-dijkstra.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2016-08-24 itempropdatePublished>August 24, 2016/time> /p> div classmedia> a classmedia-left href/post/2016/08/24/bokeh.html> img srchttp://blancosilva.github.io/images/bokeh_plot.png stylewidth:200px;> /a> div classmedia-body> a href/post/2016/08/24/bokeh.html> h4 classmedia-heading>Embedding (high quality interactive) plots and data into HTML documents with Bokeh/h4> /a> I am trying to learn a bit of Bokeh to embed plots and data into HTML documents. It looks simple enough, yet the results are pretty impressive. The example below, for instance (which is verbatim from bokeh’s own documentation), took a mere few lines of code in python. div styletext-align:right; width:100%;> a href/post/2016/08/24/bokeh.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2016-08-08 itempropdatePublished>August 08, 2016/time> /p> div classmedia> a classmedia-left href/post/2016/08/08/decanting.html> img srchttp://blancosilva.github.io/images/amphora.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2016/08/08/decanting.html> h4 classmedia-heading>Decanting Problems and Dijkstras Algorithm (II)/h4> /a> In the previous post, Decanting Problems and Dijkstra’s Algorithm, we presented some scipy hackery to solve the Die Hard puzzle: div styletext-align:right; width:100%;> a href/post/2016/08/08/decanting.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2016-07-29 itempropdatePublished>July 29, 2016/time> /p> div classmedia> a classmedia-left href/post/2016/07/29/decanting.html> img srchttp://blancosilva.github.io/images/greekjugs.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2016/07/29/decanting.html> h4 classmedia-heading>Decanting Problems and Dijkstras Algorithm/h4> /a> Decanting problems (also known as jug-pouring problems) are a set of highly entertaining classical puzzles that require some liquid to be divided in certain proportions. The challenge comes from doing so without sophisticated measuring devices. We usually have only the aid of several jugs for this purpose. The ge... div styletext-align:right; width:100%;> a href/post/2016/07/29/decanting.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-11-05 itempropdatePublished>November 05, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/11/05/Menger-Sponges.html> img srchttps://farm7.staticflickr.com/6227/6315682009_3f42068116_n_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2014/11/05/Menger-Sponges.html> h4 classmedia-heading>Menger Sponges/h4> /a> I know it is hard to grasp, but it is mathematically viable: there are solids that require an infinite amount of material to construct, yet they have no volume! Of course, having infinite surface area makes it impossible to actually build these objects, but it is feasible to come up with reasonable approximations. ... div styletext-align:right; width:100%;> a href/post/2014/11/05/Menger-Sponges.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-10-30 itempropdatePublished>October 30, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/10/30/searching-for-the-ss-central-america.html> img srchttps://farm6.staticflickr.com/5582/15072819006_39df81b2a6_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2014/10/30/searching-for-the-ss-central-america.html> h4 classmedia-heading>Searching for the SS Central America/h4> /a> On Tuesday, September 8th 1857, the steamboat SS Central America left Havana at 9 AM for New York, carrying about 600 passengers and crew members. Inside of this vessel, there was stowed a very precious cargo: a set of manuscripts by John James Audubon, and three tons of gold bars and coins. The manuscripts docum... div styletext-align:right; width:100%;> a href/post/2014/10/30/searching-for-the-ss-central-america.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-10-28 itempropdatePublished>October 28, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/10/28/Computational-Geometry-in-Python.html> img srchttp://blancosilva.github.io/images/chapter6_files/chapter6_127_0.png stylewidth:200px;> /a> div classmedia-body> a href/post/2014/10/28/Computational-Geometry-in-Python.html> h4 classmedia-heading>Computational Geometry in Python/h4> /a> This post is a simplified version of the accompanying notebook to chapter 6 of my upcoming book Mastering SciPy. Click anywhere on this box for more information. div styletext-align:right; width:100%;> a href/post/2014/10/28/Computational-Geometry-in-Python.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-07-09 itempropdatePublished>July 09, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/07/09/jotto-5-letter-mastermind-in-the-nao-robot.html> img srchttps://farm4.staticflickr.com/3910/14425999857_b6500621b4_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2014/07/09/jotto-5-letter-mastermind-in-the-nao-robot.html> h4 classmedia-heading>Jotto (5-letter Mastermind) in the NAO robot/h4> /a> I would like to show how to code the NAO robot to beat us at Jotto (5-letter Mastermind) with python in Choregraphe. I will employ a brute force technique that does not require any knowledge of the English language, the frequency of its letters, or smart combinations of vowels and consonants to try to minimize the n... div styletext-align:right; width:100%;> a href/post/2014/07/09/jotto-5-letter-mastermind-in-the-nao-robot.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-06-29 itempropdatePublished>June 29, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/06/29/robot-stories.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2014/06/29/robot-stories.html> h4 classmedia-heading>Robot stories/h4> /a> Every summer before school was over, I was assigned a list of books to read. Mostly nonfiction and historical fiction, but in fourth grade there that was that first science fiction book. I often remember how that book made me feel, and marvel at the impact that it had in my life. I had read some science fiction b... div styletext-align:right; width:100%;> a href/post/2014/06/29/robot-stories.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-03-04 itempropdatePublished>March 04, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/03/04/advanced-problem-18.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2014/03/04/advanced-problem-18.html> h4 classmedia-heading>Advanced Problem #18/h4> /a> Another fun problem, as requested by Qinfeng Li in MA598R: Measure Theory div styletext-align:right; width:100%;> a href/post/2014/03/04/advanced-problem-18.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2013-10-22 itempropdatePublished>October 22, 2013/time> /p> div classmedia> a classmedia-left href/post/2013/10/22/areas-of-mathematics.html> img srchttps://i0.wp.com/farm8.staticflickr.com/7451/10428227193_109ee4dd96_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2013/10/22/areas-of-mathematics.html> h4 classmedia-heading>Areas of Mathematics/h4> /a> For one of my upcoming talks I am trying to include an exhaustive mindmap showing the different areas of Mathematics, and somehow, how they relate to each other. Most of the information I am using has been processed from years of exposure in the field, and a bit of help from Wikipedia. div styletext-align:right; width:100%;> a href/post/2013/10/22/areas-of-mathematics.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2013-09-24 itempropdatePublished>September 24, 2013/time> /p> div classmedia> a classmedia-left href/post/2013/09/24/5927.html> img srchttp://farm3.staticflickr.com/2811/9909917143_3520006ec2_z_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2013/09/24/5927.html> h4 classmedia-heading>More on Lindenmayer Systems/h4> /a> We briefly explored Lindenmayer systems (or L-systems) in an old post: Toying with Basic Fractals. We quickly reviewed this method for creation of an approximation to fractals, and displayed an example (the Koch snowflake) based on tikz libraries. div styletext-align:right; width:100%;> a href/post/2013/09/24/5927.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2013-07-15 itempropdatePublished>July 15, 2013/time> /p> div classmedia> a classmedia-left href/post/2013/07/15/some-results-related-to-the-feuerbach-point.html> img srchttps://i0.wp.com/farm4.staticflickr.com/3805/9297168636_e56cd25e62_c.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2013/07/15/some-results-related-to-the-feuerbach-point.html> h4 classmedia-heading>Some results related to the Feuerbach Point/h4> /a> Given a triangle \( \triangle ABC \), the circle that goes through the midpoints of each side, \( D, E, F \), is called the Feuerbach circle. It has very surprising properties: div styletext-align:right; width:100%;> a href/post/2013/07/15/some-results-related-to-the-feuerbach-point.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2013-07-09 itempropdatePublished>July 09, 2013/time> /p> div classmedia> a classmedia-left href/post/2013/07/09/an-automatic-geometric-proof.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2013/07/09/an-automatic-geometric-proof.html> h4 classmedia-heading>An Automatic Geometric Proof/h4> /a> We are familiar with that result that states that, on any given triangle, the circumcenter, centroid and orthocenter are always collinear. I would like to illustrate how to use Gröbner bases theory to prove that the incenter also belongs in the previous line, provided the triangle is isosceles. div styletext-align:right; width:100%;> a href/post/2013/07/09/an-automatic-geometric-proof.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2013-06-02 itempropdatePublished>June 02, 2013/time> /p> div classmedia> a classmedia-left href/post/2013/06/02/a-nice-application-of-fatous-lemma.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2013/06/02/a-nice-application-of-fatous-lemma.html> h4 classmedia-heading>A nice application of Fatous Lemma/h4> /a> Let me show you an exciting technique to prove some convergence statements using exclusively functional inequalities and Fatou’s Lemma. The following are two classic problems solved this way. Enjoy! div styletext-align:right; width:100%;> a href/post/2013/06/02/a-nice-application-of-fatous-lemma.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2012-12-17 itempropdatePublished>December 17, 2012/time> /p> div classmedia> a classmedia-left href/post/2012/12/17/seked.html> img srchttps://i0.wp.com/farm9.staticflickr.com/8353/8279201319_00f003b2c2_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2012/12/17/seked.html> h4 classmedia-heading>Seked/h4> /a> If a pyramid is 250 cubits high and the side of its base 360 cubits long, what is its seked? div styletext-align:right; width:100%;> a href/post/2012/12/17/seked.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2012-12-14 itempropdatePublished>December 14, 2012/time> /p> div classmedia> a classmedia-left href/post/2012/12/14/nezumi-san.html> img srchttps://i0.wp.com/farm9.staticflickr.com/8074/8271874852_45aec78621_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2012/12/14/nezumi-san.html> h4 classmedia-heading>Nezumi San/h4> /a> On January first, a pair of mice appeared in a house and bore six male mice and six female mice. At the end of January there are fourteen mice: seven male and seven female. div styletext-align:right; width:100%;> a href/post/2012/12/14/nezumi-san.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2012-12-14 itempropdatePublished>December 14, 2012/time> /p> div classmedia> a classmedia-left href/post/2012/12/14/ruthless-thieves-stealing-a-roll-of-cloth.html> img srchttps://i0.wp.com/farm9.staticflickr.com/8197/8270753931_8b6b28ff06_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2012/12/14/ruthless-thieves-stealing-a-roll-of-cloth.html> h4 classmedia-heading>Ruthless Thieves Stealing a Roll of Cloth/h4> /a> Some thieves stole a long roll of silk cloth from a warehouse. In a bush far from the warehouse, they counted the length of the cloth. If each thief gets 6 hiki, then 6 hiki is left over, but if each thief takes 7 hiki then the last thief gets no cloth at all. Find the number of thieves and the length of the cl... div styletext-align:right; width:100%;> a href/post/2012/12/14/ruthless-thieves-stealing-a-roll-of-cloth.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2012-08-08 itempropdatePublished>August 08, 2012/time> /p> div classmedia> a classmedia-left href/post/2012/08/08/stones-balances-matrices.html> img srchttps://i0.wp.com/farm9.staticflickr.com/8285/7737057646_e02f559a02_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2012/08/08/stones-balances-matrices.html> h4 classmedia-heading>Stones, balances, matrices/h4> /a> We have four stones identical in size and appearance, but one of them is heavier than the rest. We have a set of scales (a balance): how many weights do we need to determine which stone is the heaviest? div styletext-align:right; width:100%;> a href/post/2012/08/08/stones-balances-matrices.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-09-26 itempropdatePublished>September 26, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/09/26/opart.html> img srchttps://i0.wp.com/farm1.static.flickr.com/52/131240309_9cfa9f61fd_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/09/26/opart.html> h4 classmedia-heading>OpArt/h4> /a> OpArt is, by definition, a style of visual art based upon optical illusions. Let it be a painting, a photograph or any other mean, the objective of this style is to play with the interaction of what you see, and what it really is. A classical OpArt piece involves confusion by giving impression of movement, imposs... div styletext-align:right; width:100%;> a href/post/2011/09/26/opart.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-09-16 itempropdatePublished>September 16, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/09/16/so-you-want-to-be-an-applied-mathematician.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2011/09/16/so-you-want-to-be-an-applied-mathematician.html> h4 classmedia-heading>So you want to be an Applied Mathematician/h4> /a> The way of the Applied Mathematician is one full of challenging and interesting problems. We thrive by association with the Pure Mathematician, and at the same time with the no-nonsense, hands-in, hard-core Engineer. But not everything is happy in Applied Mathematician land: every now and then, we receive the dis... div styletext-align:right; width:100%;> a href/post/2011/09/16/so-you-want-to-be-an-applied-mathematician.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-08-23 itempropdatePublished>August 23, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/08/23/the-ultimate-metapuzzle.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2011/08/23/the-ultimate-metapuzzle.html> h4 classmedia-heading>The ultimate metapuzzle/h4> /a> If you have been following this blog for a while, you already know of my fascination with metapuzzles. I have recently found one of the most beautiful examples of these riddles in this August’s edition of Ponder This, and following the advice of Travis, I will leave it completely open for the readers to give it a go... div styletext-align:right; width:100%;> a href/post/2011/08/23/the-ultimate-metapuzzle.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-05-08 itempropdatePublished>May 08, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/05/08/the-cantor-pairing-function.html> img srchttp://farm6.static.flickr.com/5142/5698724857_7e20970586_o.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/05/08/the-cantor-pairing-function.html> h4 classmedia-heading>The Cantor Pairing Function/h4> /a> The objective of this post is to construct a pairing function, that presents us with a bijection between the set of natural numbers, and the lattice of points in the plane with non-negative integer coordinates. div styletext-align:right; width:100%;> a href/post/2011/05/08/the-cantor-pairing-function.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-04-12 itempropdatePublished>April 12, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/04/12/el-pais-weekly-challenge.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5302/5612612083_f60c635409.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/04/12/el-pais-weekly-challenge.html> h4 classmedia-heading>El País weekly challenge/h4> /a> For a while now, the Spanish newspaper “El País” has been posing a weekly mathematical challenge to promote a collection of books, and celebrate a hundred years of their country’s Royal Mathematical Society. div styletext-align:right; width:100%;> a href/post/2011/04/12/el-pais-weekly-challenge.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-02-14 itempropdatePublished>February 14, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/02/14/math-genealogy-project.html> img srchttp://farm3.static.flickr.com/2123/2087542505_2350f768dc_m.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/02/14/math-genealogy-project.html> h4 classmedia-heading>Math Genealogy Project/h4> /a> I traced my mathematical lineage back into the XIV century at The Mathematics Genealogy Project. Imagine my surprise when I discovered that a big branch in the tree of my scientific ancestors is composed not only by mathematicians but also by big names in the fields of Physics, Chemistry, Physiology and even Anato... div styletext-align:right; width:100%;> a href/post/2011/02/14/math-genealogy-project.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-01-30 itempropdatePublished>January 30, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/01/30/apollonian-gaskets.html> img srchttp://farm6.static.flickr.com/5258/5417273431_6ab314c36e_o_d.png stylewidth:200px;> /a> div classmedia-body> a href/post/2011/01/30/apollonian-gaskets.html> h4 classmedia-heading>Apollonian gaskets and circle inversion fractals/h4> /a> Recall the definition of an iterated function system (IFS), and how on occasion, their attractors are fractal sets. What happens when we allow more general functions instead of mere affine maps? div styletext-align:right; width:100%;> a href/post/2011/01/30/apollonian-gaskets.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-01-28 itempropdatePublished>January 28, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/01/28/toying-with-basic-fractals.html> img srchttp://farm6.static.flickr.com/5132/5397495432_bb48f36b6b_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/01/28/toying-with-basic-fractals.html> h4 classmedia-heading>Toying with basic fractals/h4> /a> I will skip all the mathematical theory behind Fractals (dimensions, measures, etc) to focus directly into the description and implementation of some of the most basic examples. In this post, I will cover the ideas behind three classical techniques: div styletext-align:right; width:100%;> a href/post/2011/01/28/toying-with-basic-fractals.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-01-14 itempropdatePublished>January 14, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/01/14/basic-examples-of-maximum-likelihood-estimation.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2011/01/14/basic-examples-of-maximum-likelihood-estimation.html> h4 classmedia-heading>Basic examples of Maximum Likelihood Estimation/h4> /a> In this post, we see how to use maximum likelihood to estimate the best parameters for a few of the most common distributions. div styletext-align:right; width:100%;> a href/post/2011/01/14/basic-examples-of-maximum-likelihood-estimation.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-01-12 itempropdatePublished>January 12, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/01/12/bertrand-paradox.html> img srchttps://farm8.staticflickr.com/7526/15528806130_1944b2d5df_n_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/01/12/bertrand-paradox.html> h4 classmedia-heading>Bertrand Paradox/h4> /a> Classically, we define the probability of an event as the ratio of the favorable cases, over the number of all possible cases. Of course, these possible cases need to be all equally likely. This works great for discrete settings, like dice rolls, card games, etc. But when facing non-discrete cases, this definitio... div styletext-align:right; width:100%;> a href/post/2011/01/12/bertrand-paradox.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-16 itempropdatePublished>December 16, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/16/pick-a-point.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5121/5266694869_46b99fd46f_b_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/16/pick-a-point.html> h4 classmedia-heading>Pick a point/h4> /a> Three problems in Euclidean Geometry with a common denominator: div styletext-align:right; width:100%;> a href/post/2010/12/16/pick-a-point.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-15 itempropdatePublished>December 15, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/15/image-processing-with-numpy-scipy-and-matplotlibs-in-sage.html> img srchttp://farm6.static.flickr.com/5126/5263737296_03f9eb0224_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/15/image-processing-with-numpy-scipy-and-matplotlibs-in-sage.html> h4 classmedia-heading>Image Processing with numpy, scipy and matplotlibs in sage/h4> /a> In this post, I would like to show how to use a few different features of numpy, scipy and matplotlibs to accomplish a few basic image processing tasks: some trivial image manipulation, segmentation, obtaining of structural information, etc. An excellent way to show a good set of these techniques is by working thr... div styletext-align:right; width:100%;> a href/post/2010/12/15/image-processing-with-numpy-scipy-and-matplotlibs-in-sage.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-12 itempropdatePublished>December 12, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/12/using-tikz-as-an-igse.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5287/5253671077_cb653de83c_b_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/12/using-tikz-as-an-igse.html> h4 classmedia-heading>Using tikz as an IGSE/h4> /a> An IGSE (Interactive Geometry Software Environment) is a computer program that helps you create dynamic diagrams in different Geometries (planar or 3D Euclidean, or even spherical or hyperbolic!). Click here and there to drop points, select two and construct the segment through them, or the circle centered in the f... div styletext-align:right; width:100%;> a href/post/2010/12/12/using-tikz-as-an-igse.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-09 itempropdatePublished>December 09, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/09/interaction-with-sage.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5041/5246735458_d7e745531c_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/09/interaction-with-sage.html> h4 classmedia-heading>Interaction with Sage/h4> /a> The objective of this post is to show a few examples of interaction of sage with \( \LaTeX \) to produce results that, otherwise, would carry extensive writing and computation on the side. We will base it on the figure from the post Sequence of Right Triangles, where right triangles were constructed by halving one... div styletext-align:right; width:100%;> a href/post/2010/12/09/interaction-with-sage.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-03 itempropdatePublished>December 03, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/03/application-packages.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5282/5229308197_b154d1ccae_m_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/03/application-packages.html> h4 classmedia-heading>Application Packages/h4> /a> The problem at hand is the following: a few months before graduation, a Ph.D. candidate usually sends hundreds of application packages to different universities, research institutions and companies, with the intention of gaining a profitable job. We all agree that the process is certainly painful: gathering referen... div styletext-align:right; width:100%;> a href/post/2010/12/03/application-packages.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-01 itempropdatePublished>December 01, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/01/fixed-point-theorems.html> img srchttp://farm6.static.flickr.com/5208/5224985241_813dab62b3_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/01/fixed-point-theorems.html> h4 classmedia-heading>Borsuk-Ulam and Fixed Point Theorems/h4> /a> At any given moment on the surface of the Earth there are always two antipodal points with exactly the same temperature and barometric pressure. We can go even further: on each longitude (the North and South lines running from pole to pole) there will also be two antipodal points sharing exactly the same temperatur... div styletext-align:right; width:100%;> a href/post/2010/12/01/fixed-point-theorems.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-11-22 itempropdatePublished>November 22, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/11/22/sequence-of-right-triangles.html> img srchttp://farm6.static.flickr.com/5127/5200460444_a4f4b16a39_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/11/22/sequence-of-right-triangles.html> h4 classmedia-heading>Sequence of right triangles/h4> /a> Consider the right triangle \(\triangle_1 \) with vertices at \((0,0) \), \((0,1) \), and \((1,1). \) Note that the angle at the origin is \(\frac{\pi}{4}. \) Use the hypotenuse of \(\triangle_1 \) as one of the legs of another right triangle, \(\triangle_2, \) with an angle of \(\frac{\pi}{8} \) at the origin,... div styletext-align:right; width:100%;> a href/post/2010/11/22/sequence-of-right-triangles.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-11-21 itempropdatePublished>November 21, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/11/21/points-on-a-plane.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5161/5195162552_f8523866e3_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/11/21/points-on-a-plane.html> h4 classmedia-heading>Points on a plane/h4> /a> A few puzzles about sets of points, and a nice conjecture following up one of those questions: div styletext-align:right; width:100%;> a href/post/2010/11/21/points-on-a-plane.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-11-15 itempropdatePublished>November 15, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/11/15/chess-puzzles.html> img srchttps://i0.wp.com/farm2.static.flickr.com/1257/5179790956_17a83f79fd_b_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/11/15/chess-puzzles.html> h4 classmedia-heading>Chess puzzles/h4> /a> It is no surprise that the game of chess generates such an amount of mathematical puzzles. The amount of riddles of combinatoric nature alone should have the readers busy for a long while, no matter what their chess strength is. This is a selection of several puzzles designed with that purpose in mind. div styletext-align:right; width:100%;> a href/post/2010/11/15/chess-puzzles.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-11-15 itempropdatePublished>November 15, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/11/15/exact-expression.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2010/11/15/exact-expression.html> h4 classmedia-heading>Exact Expression/h4> /a> A nice problem to find a closed form for a rather challenging infinite series. Can you get it without using a computer? div styletext-align:right; width:100%;> a href/post/2010/11/15/exact-expression.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-11-08 itempropdatePublished>November 08, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/11/08/what-day-of-the-week.html> img srchttp://farm5.static.flickr.com/4091/5157027232_5364aa4ef0_b_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/11/08/what-day-of-the-week.html> h4 classmedia-heading>What day of the week?/h4> /a> What day of the week was I born? Getting a calendar of that year could prove an impossible task, although if you are in front of a computer, there are *nix utilities that will do that for you. But seriously, who has access to a computer with unix or linux when the question pops? div styletext-align:right; width:100%;> a href/post/2010/11/08/what-day-of-the-week.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-22 itempropdatePublished>October 22, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/22/the-cantor-set.html> img srchttp://farm2.static.flickr.com/1155/5105641217_ec5cf35a93_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/10/22/the-cantor-set.html> h4 classmedia-heading>The Cantor Set/h4> /a> Consider the unit interval in the real line, \( 0,1 \), and remove the middle third open subinterval \( (1/3, 2/3) \). We have the closed set \( C_1 0,1/3 \cup 2/3,1 \), which is the union of two closed intervals. In a second step, remove the middle third open subintervals of each of the previous two inter... div styletext-align:right; width:100%;> a href/post/2010/10/22/the-cantor-set.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-22 itempropdatePublished>October 22, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/22/jordan-curve-theorem.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2010/10/22/jordan-curve-theorem.html> h4 classmedia-heading>The Jordan Curve Theorem/h4> /a> The first time I faced this challenge was in the stage of my second Analysis course in College. The instructor needed this result for one of the proofs in class, stated it, and claimed that “you would need some more miles under your belts to be able to find—and understand—a proof of it.” It goes like this: div styletext-align:right; width:100%;> a href/post/2010/10/22/jordan-curve-theorem.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-22 itempropdatePublished>October 22, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/22/thieves.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2010/10/22/thieves.html> h4 classmedia-heading>Thieves!/h4> /a> These are from Smullyan’s “The Riddle of Scheherazade”. They are of mathematical nature, and serve for appetizers to a nice collection of logic riddles. They go like this: div styletext-align:right; width:100%;> a href/post/2010/10/22/thieves.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-20 itempropdatePublished>October 20, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/20/convex-triangle-square-polygons.html> img srchttps://i0.wp.com/farm2.static.flickr.com/1316/5101252276_83447d2752_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/10/20/convex-triangle-square-polygons.html> h4 classmedia-heading>Convex triangle-square polygons/h4> /a> Consider an infinite supply of cardboard equilateral triangles and squares, all of them with side length of one inch. With these pieces, we desire to form convex polygons of different sides. It is trivial to come up with this kind of polygons for sides 3, 4, 5 and 6. Construct examples of these convex p... div styletext-align:right; width:100%;> a href/post/2010/10/20/convex-triangle-square-polygons.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-20 itempropdatePublished>October 20, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/20/probability-and-divisibility-by-11.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2010/10/20/probability-and-divisibility-by-11.html> h4 classmedia-heading>Probability and Divisibility by 11/h4> /a> Seven different playing cards, with values from ace to seven, are shaken in a hat, then taken out singly and then placed in a row. What is the probability that this seven-digit number is divisible by 11? div styletext-align:right; width:100%;> a href/post/2010/10/20/probability-and-divisibility-by-11.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-15 itempropdatePublished>October 15, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/15/what-is-the-next-number.html> img srchttps://i0.wp.com/farm5.static.flickr.com/4132/5084588268_0a448b9d35_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/10/15/what-is-the-next-number.html> h4 classmedia-heading>What is the next number?/h4> /a> A classical problem involving ordered lists of numbers. What is the next term in the following sequence? div styletext-align:right; width:100%;> a href/post/2010/10/15/what-is-the-next-number.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-14 itempropdatePublished>October 14, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/14/a-geometric-fallacy.html> img srchttp://farm5.static.flickr.com/4041/5081312425_6ebb5b2376_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/10/14/a-geometric-fallacy.html> h4 classmedia-heading>A geometric fallacy/h4> /a> A geometric fallacy is basically a geometric construction that leads to a false result. I once found an obscure russian treatise on this matter (published by мир), that kept me entertained for weeks: Ya.S.Dubnov’s Errores en las demostraciones geométricas. The edition I have is a decent translation into Spanish, m... div styletext-align:right; width:100%;> a href/post/2010/10/14/a-geometric-fallacy.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-13 itempropdatePublished>October 13, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/13/my-oldest-plays-the-piano.html> img srchttps://farm9.staticflickr.com/8678/15682120759_257ce44a5c_n_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/10/13/my-oldest-plays-the-piano.html> h4 classmedia-heading>My oldest plays the piano!/h4> /a> Two old friends, Ernie and Bernie, bump into each other in the street. It was more than twenty years since they last saw each other, so they decide to spend some time together in a nearby coffee shop, catching up. At some point, Bernie asks the inevitable: So, you got married? div styletext-align:right; width:100%;> a href/post/2010/10/13/my-oldest-plays-the-piano.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-04-28 itempropdatePublished>April 28, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/04/28/the-nonlocal-means-algorithm.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2010/04/28/the-nonlocal-means-algorithm.html> h4 classmedia-heading>The Nonlocal-means Algorithm/h4> /a> The nonlocal-means algorithm Buades, Coll, Morel was designed to perform noise reduction on digital images, while preserving the main geometrical configurations, as well as finer structures, details and texture. The algorithm is consistent under the condition that one can find many samples of every image detail w... div styletext-align:right; width:100%;> a href/post/2010/04/28/the-nonlocal-means-algorithm.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2008-09-27 itempropdatePublished>September 27, 2008/time> /p> div classmedia> a classmedia-left href/post/2008/09/27/the-hunt-for-a-bellman-function-2.html> img srchttp://farm3.static.flickr.com/2602/4047407579_8397368be9_o.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2008/09/27/the-hunt-for-a-bellman-function-2.html> h4 classmedia-heading>The hunt for a Bellman Function./h4> /a> This is a beautiful and powerful mathematical technique in Harmonic Analysis that allows, among other things, to prove very complicated inequalities in the theory of Singular Integral Operators, without using much of the classical machinery in this field. div styletext-align:right; width:100%;> a href/post/2008/09/27/the-hunt-for-a-bellman-function-2.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2007-08-05 itempropdatePublished>August 05, 2007/time> /p> div classmedia> a classmedia-left href/post/2007/08/05/mechanical-geometry-theorem-proving.html> img srchttp://farm1.static.flickr.com/113/298203907_77bcce2162.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2007/08/05/mechanical-geometry-theorem-proving.html> h4 classmedia-heading>Mechanical Geometry Theorem Proving/h4> /a> In 1977, Professor Wen-Tsun Wu succeeded in developing a method of mechanical geometry theorem proving. This method has been applied to prove or even discover hundreds of non-trivial difficult theorems in elementary and differential geometries on a computer in an almost trivial manner. 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A quick... div styletext-align:right; width:100%;> a href/post/2016/09/10/periodic-table.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2016-09-04 itempropdatePublished>September 04, 2016/time> /p> div classmedia> a classmedia-left href/post/2016/09/04/bokeh-dijkstra.html> img srchttp://blancosilva.github.io/images/bokeh-dijkstra.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2016/09/04/bokeh-dijkstra.html> h4 classmedia-heading>Interactive Shortest-distance calculations on Triangulations/h4> /a> As a means to bring attention to my latest book, Mastering SciPy, I wrote a blog post summarizing some of the techniques illustrated in one of its chapters: Computational Geometry in Python. On that post, I created an example of computation of shortest distances between two vertices of the constrained conforming De... div styletext-align:right; width:100%;> a href/post/2016/09/04/bokeh-dijkstra.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2016-08-24 itempropdatePublished>August 24, 2016/time> /p> div classmedia> a classmedia-left href/post/2016/08/24/bokeh.html> img srchttp://blancosilva.github.io/images/bokeh_plot.png stylewidth:200px;> /a> div classmedia-body> a href/post/2016/08/24/bokeh.html> h4 classmedia-heading>Embedding (high quality interactive) plots and data into HTML documents with Bokeh/h4> /a> I am trying to learn a bit of Bokeh to embed plots and data into HTML documents. It looks simple enough, yet the results are pretty impressive. The example below, for instance (which is verbatim from bokeh’s own documentation), took a mere few lines of code in python. div styletext-align:right; width:100%;> a href/post/2016/08/24/bokeh.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2016-08-08 itempropdatePublished>August 08, 2016/time> /p> div classmedia> a classmedia-left href/post/2016/08/08/decanting.html> img srchttp://blancosilva.github.io/images/amphora.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2016/08/08/decanting.html> h4 classmedia-heading>Decanting Problems and Dijkstras Algorithm (II)/h4> /a> In the previous post, Decanting Problems and Dijkstra’s Algorithm, we presented some scipy hackery to solve the Die Hard puzzle: div styletext-align:right; width:100%;> a href/post/2016/08/08/decanting.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2016-07-29 itempropdatePublished>July 29, 2016/time> /p> div classmedia> a classmedia-left href/post/2016/07/29/decanting.html> img srchttp://blancosilva.github.io/images/greekjugs.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2016/07/29/decanting.html> h4 classmedia-heading>Decanting Problems and Dijkstras Algorithm/h4> /a> Decanting problems (also known as jug-pouring problems) are a set of highly entertaining classical puzzles that require some liquid to be divided in certain proportions. The challenge comes from doing so without sophisticated measuring devices. We usually have only the aid of several jugs for this purpose. The ge... div styletext-align:right; width:100%;> a href/post/2016/07/29/decanting.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-11-05 itempropdatePublished>November 05, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/11/05/Menger-Sponges.html> img srchttps://farm7.staticflickr.com/6227/6315682009_3f42068116_n_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2014/11/05/Menger-Sponges.html> h4 classmedia-heading>Menger Sponges/h4> /a> I know it is hard to grasp, but it is mathematically viable: there are solids that require an infinite amount of material to construct, yet they have no volume! Of course, having infinite surface area makes it impossible to actually build these objects, but it is feasible to come up with reasonable approximations. ... div styletext-align:right; width:100%;> a href/post/2014/11/05/Menger-Sponges.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-10-30 itempropdatePublished>October 30, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/10/30/searching-for-the-ss-central-america.html> img srchttps://farm6.staticflickr.com/5582/15072819006_39df81b2a6_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2014/10/30/searching-for-the-ss-central-america.html> h4 classmedia-heading>Searching for the SS Central America/h4> /a> On Tuesday, September 8th 1857, the steamboat SS Central America left Havana at 9 AM for New York, carrying about 600 passengers and crew members. Inside of this vessel, there was stowed a very precious cargo: a set of manuscripts by John James Audubon, and three tons of gold bars and coins. The manuscripts docum... div styletext-align:right; width:100%;> a href/post/2014/10/30/searching-for-the-ss-central-america.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-10-28 itempropdatePublished>October 28, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/10/28/Computational-Geometry-in-Python.html> img srchttp://blancosilva.github.io/images/chapter6_files/chapter6_127_0.png stylewidth:200px;> /a> div classmedia-body> a href/post/2014/10/28/Computational-Geometry-in-Python.html> h4 classmedia-heading>Computational Geometry in Python/h4> /a> This post is a simplified version of the accompanying notebook to chapter 6 of my upcoming book Mastering SciPy. Click anywhere on this box for more information. div styletext-align:right; width:100%;> a href/post/2014/10/28/Computational-Geometry-in-Python.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-07-09 itempropdatePublished>July 09, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/07/09/jotto-5-letter-mastermind-in-the-nao-robot.html> img srchttps://farm4.staticflickr.com/3910/14425999857_b6500621b4_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2014/07/09/jotto-5-letter-mastermind-in-the-nao-robot.html> h4 classmedia-heading>Jotto (5-letter Mastermind) in the NAO robot/h4> /a> I would like to show how to code the NAO robot to beat us at Jotto (5-letter Mastermind) with python in Choregraphe. I will employ a brute force technique that does not require any knowledge of the English language, the frequency of its letters, or smart combinations of vowels and consonants to try to minimize the n... div styletext-align:right; width:100%;> a href/post/2014/07/09/jotto-5-letter-mastermind-in-the-nao-robot.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-06-29 itempropdatePublished>June 29, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/06/29/robot-stories.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2014/06/29/robot-stories.html> h4 classmedia-heading>Robot stories/h4> /a> Every summer before school was over, I was assigned a list of books to read. Mostly nonfiction and historical fiction, but in fourth grade there that was that first science fiction book. I often remember how that book made me feel, and marvel at the impact that it had in my life. I had read some science fiction b... div styletext-align:right; width:100%;> a href/post/2014/06/29/robot-stories.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2014-03-04 itempropdatePublished>March 04, 2014/time> /p> div classmedia> a classmedia-left href/post/2014/03/04/advanced-problem-18.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2014/03/04/advanced-problem-18.html> h4 classmedia-heading>Advanced Problem #18/h4> /a> Another fun problem, as requested by Qinfeng Li in MA598R: Measure Theory div styletext-align:right; width:100%;> a href/post/2014/03/04/advanced-problem-18.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2013-10-22 itempropdatePublished>October 22, 2013/time> /p> div classmedia> a classmedia-left href/post/2013/10/22/areas-of-mathematics.html> img srchttps://i0.wp.com/farm8.staticflickr.com/7451/10428227193_109ee4dd96_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2013/10/22/areas-of-mathematics.html> h4 classmedia-heading>Areas of Mathematics/h4> /a> For one of my upcoming talks I am trying to include an exhaustive mindmap showing the different areas of Mathematics, and somehow, how they relate to each other. Most of the information I am using has been processed from years of exposure in the field, and a bit of help from Wikipedia. div styletext-align:right; width:100%;> a href/post/2013/10/22/areas-of-mathematics.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2013-09-24 itempropdatePublished>September 24, 2013/time> /p> div classmedia> a classmedia-left href/post/2013/09/24/5927.html> img srchttp://farm3.staticflickr.com/2811/9909917143_3520006ec2_z_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2013/09/24/5927.html> h4 classmedia-heading>More on Lindenmayer Systems/h4> /a> We briefly explored Lindenmayer systems (or L-systems) in an old post: Toying with Basic Fractals. We quickly reviewed this method for creation of an approximation to fractals, and displayed an example (the Koch snowflake) based on tikz libraries. div styletext-align:right; width:100%;> a href/post/2013/09/24/5927.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2013-07-15 itempropdatePublished>July 15, 2013/time> /p> div classmedia> a classmedia-left href/post/2013/07/15/some-results-related-to-the-feuerbach-point.html> img srchttps://i0.wp.com/farm4.staticflickr.com/3805/9297168636_e56cd25e62_c.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2013/07/15/some-results-related-to-the-feuerbach-point.html> h4 classmedia-heading>Some results related to the Feuerbach Point/h4> /a> Given a triangle \( \triangle ABC \), the circle that goes through the midpoints of each side, \( D, E, F \), is called the Feuerbach circle. It has very surprising properties: div styletext-align:right; width:100%;> a href/post/2013/07/15/some-results-related-to-the-feuerbach-point.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2013-07-09 itempropdatePublished>July 09, 2013/time> /p> div classmedia> a classmedia-left href/post/2013/07/09/an-automatic-geometric-proof.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2013/07/09/an-automatic-geometric-proof.html> h4 classmedia-heading>An Automatic Geometric Proof/h4> /a> We are familiar with that result that states that, on any given triangle, the circumcenter, centroid and orthocenter are always collinear. I would like to illustrate how to use Gröbner bases theory to prove that the incenter also belongs in the previous line, provided the triangle is isosceles. div styletext-align:right; width:100%;> a href/post/2013/07/09/an-automatic-geometric-proof.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2013-06-02 itempropdatePublished>June 02, 2013/time> /p> div classmedia> a classmedia-left href/post/2013/06/02/a-nice-application-of-fatous-lemma.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2013/06/02/a-nice-application-of-fatous-lemma.html> h4 classmedia-heading>A nice application of Fatous Lemma/h4> /a> Let me show you an exciting technique to prove some convergence statements using exclusively functional inequalities and Fatou’s Lemma. The following are two classic problems solved this way. Enjoy! div styletext-align:right; width:100%;> a href/post/2013/06/02/a-nice-application-of-fatous-lemma.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2012-12-17 itempropdatePublished>December 17, 2012/time> /p> div classmedia> a classmedia-left href/post/2012/12/17/seked.html> img srchttps://i0.wp.com/farm9.staticflickr.com/8353/8279201319_00f003b2c2_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2012/12/17/seked.html> h4 classmedia-heading>Seked/h4> /a> If a pyramid is 250 cubits high and the side of its base 360 cubits long, what is its seked? div styletext-align:right; width:100%;> a href/post/2012/12/17/seked.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2012-12-14 itempropdatePublished>December 14, 2012/time> /p> div classmedia> a classmedia-left href/post/2012/12/14/nezumi-san.html> img srchttps://i0.wp.com/farm9.staticflickr.com/8074/8271874852_45aec78621_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2012/12/14/nezumi-san.html> h4 classmedia-heading>Nezumi San/h4> /a> On January first, a pair of mice appeared in a house and bore six male mice and six female mice. At the end of January there are fourteen mice: seven male and seven female. div styletext-align:right; width:100%;> a href/post/2012/12/14/nezumi-san.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2012-12-14 itempropdatePublished>December 14, 2012/time> /p> div classmedia> a classmedia-left href/post/2012/12/14/ruthless-thieves-stealing-a-roll-of-cloth.html> img srchttps://i0.wp.com/farm9.staticflickr.com/8197/8270753931_8b6b28ff06_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2012/12/14/ruthless-thieves-stealing-a-roll-of-cloth.html> h4 classmedia-heading>Ruthless Thieves Stealing a Roll of Cloth/h4> /a> Some thieves stole a long roll of silk cloth from a warehouse. In a bush far from the warehouse, they counted the length of the cloth. If each thief gets 6 hiki, then 6 hiki is left over, but if each thief takes 7 hiki then the last thief gets no cloth at all. Find the number of thieves and the length of the cl... div styletext-align:right; width:100%;> a href/post/2012/12/14/ruthless-thieves-stealing-a-roll-of-cloth.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2012-08-08 itempropdatePublished>August 08, 2012/time> /p> div classmedia> a classmedia-left href/post/2012/08/08/stones-balances-matrices.html> img srchttps://i0.wp.com/farm9.staticflickr.com/8285/7737057646_e02f559a02_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2012/08/08/stones-balances-matrices.html> h4 classmedia-heading>Stones, balances, matrices/h4> /a> We have four stones identical in size and appearance, but one of them is heavier than the rest. We have a set of scales (a balance): how many weights do we need to determine which stone is the heaviest? div styletext-align:right; width:100%;> a href/post/2012/08/08/stones-balances-matrices.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-09-26 itempropdatePublished>September 26, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/09/26/opart.html> img srchttps://i0.wp.com/farm1.static.flickr.com/52/131240309_9cfa9f61fd_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/09/26/opart.html> h4 classmedia-heading>OpArt/h4> /a> OpArt is, by definition, a style of visual art based upon optical illusions. Let it be a painting, a photograph or any other mean, the objective of this style is to play with the interaction of what you see, and what it really is. A classical OpArt piece involves confusion by giving impression of movement, imposs... div styletext-align:right; width:100%;> a href/post/2011/09/26/opart.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-09-16 itempropdatePublished>September 16, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/09/16/so-you-want-to-be-an-applied-mathematician.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2011/09/16/so-you-want-to-be-an-applied-mathematician.html> h4 classmedia-heading>So you want to be an Applied Mathematician/h4> /a> The way of the Applied Mathematician is one full of challenging and interesting problems. We thrive by association with the Pure Mathematician, and at the same time with the no-nonsense, hands-in, hard-core Engineer. But not everything is happy in Applied Mathematician land: every now and then, we receive the dis... div styletext-align:right; width:100%;> a href/post/2011/09/16/so-you-want-to-be-an-applied-mathematician.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-08-23 itempropdatePublished>August 23, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/08/23/the-ultimate-metapuzzle.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2011/08/23/the-ultimate-metapuzzle.html> h4 classmedia-heading>The ultimate metapuzzle/h4> /a> If you have been following this blog for a while, you already know of my fascination with metapuzzles. I have recently found one of the most beautiful examples of these riddles in this August’s edition of Ponder This, and following the advice of Travis, I will leave it completely open for the readers to give it a go... div styletext-align:right; width:100%;> a href/post/2011/08/23/the-ultimate-metapuzzle.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-05-08 itempropdatePublished>May 08, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/05/08/the-cantor-pairing-function.html> img srchttp://farm6.static.flickr.com/5142/5698724857_7e20970586_o.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/05/08/the-cantor-pairing-function.html> h4 classmedia-heading>The Cantor Pairing Function/h4> /a> The objective of this post is to construct a pairing function, that presents us with a bijection between the set of natural numbers, and the lattice of points in the plane with non-negative integer coordinates. div styletext-align:right; width:100%;> a href/post/2011/05/08/the-cantor-pairing-function.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-04-12 itempropdatePublished>April 12, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/04/12/el-pais-weekly-challenge.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5302/5612612083_f60c635409.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/04/12/el-pais-weekly-challenge.html> h4 classmedia-heading>El País weekly challenge/h4> /a> For a while now, the Spanish newspaper “El País” has been posing a weekly mathematical challenge to promote a collection of books, and celebrate a hundred years of their country’s Royal Mathematical Society. div styletext-align:right; width:100%;> a href/post/2011/04/12/el-pais-weekly-challenge.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-02-14 itempropdatePublished>February 14, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/02/14/math-genealogy-project.html> img srchttp://farm3.static.flickr.com/2123/2087542505_2350f768dc_m.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/02/14/math-genealogy-project.html> h4 classmedia-heading>Math Genealogy Project/h4> /a> I traced my mathematical lineage back into the XIV century at The Mathematics Genealogy Project. Imagine my surprise when I discovered that a big branch in the tree of my scientific ancestors is composed not only by mathematicians but also by big names in the fields of Physics, Chemistry, Physiology and even Anato... div styletext-align:right; width:100%;> a href/post/2011/02/14/math-genealogy-project.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-01-30 itempropdatePublished>January 30, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/01/30/apollonian-gaskets.html> img srchttp://farm6.static.flickr.com/5258/5417273431_6ab314c36e_o_d.png stylewidth:200px;> /a> div classmedia-body> a href/post/2011/01/30/apollonian-gaskets.html> h4 classmedia-heading>Apollonian gaskets and circle inversion fractals/h4> /a> Recall the definition of an iterated function system (IFS), and how on occasion, their attractors are fractal sets. What happens when we allow more general functions instead of mere affine maps? div styletext-align:right; width:100%;> a href/post/2011/01/30/apollonian-gaskets.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-01-28 itempropdatePublished>January 28, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/01/28/toying-with-basic-fractals.html> img srchttp://farm6.static.flickr.com/5132/5397495432_bb48f36b6b_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/01/28/toying-with-basic-fractals.html> h4 classmedia-heading>Toying with basic fractals/h4> /a> I will skip all the mathematical theory behind Fractals (dimensions, measures, etc) to focus directly into the description and implementation of some of the most basic examples. In this post, I will cover the ideas behind three classical techniques: div styletext-align:right; width:100%;> a href/post/2011/01/28/toying-with-basic-fractals.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-01-14 itempropdatePublished>January 14, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/01/14/basic-examples-of-maximum-likelihood-estimation.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2011/01/14/basic-examples-of-maximum-likelihood-estimation.html> h4 classmedia-heading>Basic examples of Maximum Likelihood Estimation/h4> /a> In this post, we see how to use maximum likelihood to estimate the best parameters for a few of the most common distributions. div styletext-align:right; width:100%;> a href/post/2011/01/14/basic-examples-of-maximum-likelihood-estimation.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2011-01-12 itempropdatePublished>January 12, 2011/time> /p> div classmedia> a classmedia-left href/post/2011/01/12/bertrand-paradox.html> img srchttps://farm8.staticflickr.com/7526/15528806130_1944b2d5df_n_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2011/01/12/bertrand-paradox.html> h4 classmedia-heading>Bertrand Paradox/h4> /a> Classically, we define the probability of an event as the ratio of the favorable cases, over the number of all possible cases. Of course, these possible cases need to be all equally likely. This works great for discrete settings, like dice rolls, card games, etc. But when facing non-discrete cases, this definitio... div styletext-align:right; width:100%;> a href/post/2011/01/12/bertrand-paradox.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-16 itempropdatePublished>December 16, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/16/pick-a-point.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5121/5266694869_46b99fd46f_b_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/16/pick-a-point.html> h4 classmedia-heading>Pick a point/h4> /a> Three problems in Euclidean Geometry with a common denominator: div styletext-align:right; width:100%;> a href/post/2010/12/16/pick-a-point.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-15 itempropdatePublished>December 15, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/15/image-processing-with-numpy-scipy-and-matplotlibs-in-sage.html> img srchttp://farm6.static.flickr.com/5126/5263737296_03f9eb0224_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/15/image-processing-with-numpy-scipy-and-matplotlibs-in-sage.html> h4 classmedia-heading>Image Processing with numpy, scipy and matplotlibs in sage/h4> /a> In this post, I would like to show how to use a few different features of numpy, scipy and matplotlibs to accomplish a few basic image processing tasks: some trivial image manipulation, segmentation, obtaining of structural information, etc. An excellent way to show a good set of these techniques is by working thr... div styletext-align:right; width:100%;> a href/post/2010/12/15/image-processing-with-numpy-scipy-and-matplotlibs-in-sage.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-12 itempropdatePublished>December 12, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/12/using-tikz-as-an-igse.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5287/5253671077_cb653de83c_b_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/12/using-tikz-as-an-igse.html> h4 classmedia-heading>Using tikz as an IGSE/h4> /a> An IGSE (Interactive Geometry Software Environment) is a computer program that helps you create dynamic diagrams in different Geometries (planar or 3D Euclidean, or even spherical or hyperbolic!). Click here and there to drop points, select two and construct the segment through them, or the circle centered in the f... div styletext-align:right; width:100%;> a href/post/2010/12/12/using-tikz-as-an-igse.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-09 itempropdatePublished>December 09, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/09/interaction-with-sage.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5041/5246735458_d7e745531c_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/09/interaction-with-sage.html> h4 classmedia-heading>Interaction with Sage/h4> /a> The objective of this post is to show a few examples of interaction of sage with \( \LaTeX \) to produce results that, otherwise, would carry extensive writing and computation on the side. We will base it on the figure from the post Sequence of Right Triangles, where right triangles were constructed by halving one... div styletext-align:right; width:100%;> a href/post/2010/12/09/interaction-with-sage.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-03 itempropdatePublished>December 03, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/03/application-packages.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5282/5229308197_b154d1ccae_m_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/03/application-packages.html> h4 classmedia-heading>Application Packages/h4> /a> The problem at hand is the following: a few months before graduation, a Ph.D. candidate usually sends hundreds of application packages to different universities, research institutions and companies, with the intention of gaining a profitable job. We all agree that the process is certainly painful: gathering referen... div styletext-align:right; width:100%;> a href/post/2010/12/03/application-packages.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-12-01 itempropdatePublished>December 01, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/12/01/fixed-point-theorems.html> img srchttp://farm6.static.flickr.com/5208/5224985241_813dab62b3_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/12/01/fixed-point-theorems.html> h4 classmedia-heading>Borsuk-Ulam and Fixed Point Theorems/h4> /a> At any given moment on the surface of the Earth there are always two antipodal points with exactly the same temperature and barometric pressure. We can go even further: on each longitude (the North and South lines running from pole to pole) there will also be two antipodal points sharing exactly the same temperatur... div styletext-align:right; width:100%;> a href/post/2010/12/01/fixed-point-theorems.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-11-22 itempropdatePublished>November 22, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/11/22/sequence-of-right-triangles.html> img srchttp://farm6.static.flickr.com/5127/5200460444_a4f4b16a39_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/11/22/sequence-of-right-triangles.html> h4 classmedia-heading>Sequence of right triangles/h4> /a> Consider the right triangle \(\triangle_1 \) with vertices at \((0,0) \), \((0,1) \), and \((1,1). \) Note that the angle at the origin is \(\frac{\pi}{4}. \) Use the hypotenuse of \(\triangle_1 \) as one of the legs of another right triangle, \(\triangle_2, \) with an angle of \(\frac{\pi}{8} \) at the origin,... div styletext-align:right; width:100%;> a href/post/2010/11/22/sequence-of-right-triangles.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-11-21 itempropdatePublished>November 21, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/11/21/points-on-a-plane.html> img srchttps://i0.wp.com/farm6.static.flickr.com/5161/5195162552_f8523866e3_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/11/21/points-on-a-plane.html> h4 classmedia-heading>Points on a plane/h4> /a> A few puzzles about sets of points, and a nice conjecture following up one of those questions: div styletext-align:right; width:100%;> a href/post/2010/11/21/points-on-a-plane.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-11-15 itempropdatePublished>November 15, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/11/15/chess-puzzles.html> img srchttps://i0.wp.com/farm2.static.flickr.com/1257/5179790956_17a83f79fd_b_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/11/15/chess-puzzles.html> h4 classmedia-heading>Chess puzzles/h4> /a> It is no surprise that the game of chess generates such an amount of mathematical puzzles. The amount of riddles of combinatoric nature alone should have the readers busy for a long while, no matter what their chess strength is. This is a selection of several puzzles designed with that purpose in mind. div styletext-align:right; width:100%;> a href/post/2010/11/15/chess-puzzles.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-11-15 itempropdatePublished>November 15, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/11/15/exact-expression.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2010/11/15/exact-expression.html> h4 classmedia-heading>Exact Expression/h4> /a> A nice problem to find a closed form for a rather challenging infinite series. Can you get it without using a computer? div styletext-align:right; width:100%;> a href/post/2010/11/15/exact-expression.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-11-08 itempropdatePublished>November 08, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/11/08/what-day-of-the-week.html> img srchttp://farm5.static.flickr.com/4091/5157027232_5364aa4ef0_b_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/11/08/what-day-of-the-week.html> h4 classmedia-heading>What day of the week?/h4> /a> What day of the week was I born? Getting a calendar of that year could prove an impossible task, although if you are in front of a computer, there are *nix utilities that will do that for you. But seriously, who has access to a computer with unix or linux when the question pops? div styletext-align:right; width:100%;> a href/post/2010/11/08/what-day-of-the-week.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-22 itempropdatePublished>October 22, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/22/the-cantor-set.html> img srchttp://farm2.static.flickr.com/1155/5105641217_ec5cf35a93_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/10/22/the-cantor-set.html> h4 classmedia-heading>The Cantor Set/h4> /a> Consider the unit interval in the real line, \( 0,1 \), and remove the middle third open subinterval \( (1/3, 2/3) \). We have the closed set \( C_1 0,1/3 \cup 2/3,1 \), which is the union of two closed intervals. In a second step, remove the middle third open subintervals of each of the previous two inter... div styletext-align:right; width:100%;> a href/post/2010/10/22/the-cantor-set.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-22 itempropdatePublished>October 22, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/22/jordan-curve-theorem.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2010/10/22/jordan-curve-theorem.html> h4 classmedia-heading>The Jordan Curve Theorem/h4> /a> The first time I faced this challenge was in the stage of my second Analysis course in College. The instructor needed this result for one of the proofs in class, stated it, and claimed that “you would need some more miles under your belts to be able to find—and understand—a proof of it.” It goes like this: div styletext-align:right; width:100%;> a href/post/2010/10/22/jordan-curve-theorem.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-22 itempropdatePublished>October 22, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/22/thieves.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2010/10/22/thieves.html> h4 classmedia-heading>Thieves!/h4> /a> These are from Smullyan’s “The Riddle of Scheherazade”. They are of mathematical nature, and serve for appetizers to a nice collection of logic riddles. They go like this: div styletext-align:right; width:100%;> a href/post/2010/10/22/thieves.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-20 itempropdatePublished>October 20, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/20/convex-triangle-square-polygons.html> img srchttps://i0.wp.com/farm2.static.flickr.com/1316/5101252276_83447d2752_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/10/20/convex-triangle-square-polygons.html> h4 classmedia-heading>Convex triangle-square polygons/h4> /a> Consider an infinite supply of cardboard equilateral triangles and squares, all of them with side length of one inch. With these pieces, we desire to form convex polygons of different sides. It is trivial to come up with this kind of polygons for sides 3, 4, 5 and 6. Construct examples of these convex p... div styletext-align:right; width:100%;> a href/post/2010/10/20/convex-triangle-square-polygons.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-20 itempropdatePublished>October 20, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/20/probability-and-divisibility-by-11.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2010/10/20/probability-and-divisibility-by-11.html> h4 classmedia-heading>Probability and Divisibility by 11/h4> /a> Seven different playing cards, with values from ace to seven, are shaken in a hat, then taken out singly and then placed in a row. What is the probability that this seven-digit number is divisible by 11? div styletext-align:right; width:100%;> a href/post/2010/10/20/probability-and-divisibility-by-11.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-15 itempropdatePublished>October 15, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/15/what-is-the-next-number.html> img srchttps://i0.wp.com/farm5.static.flickr.com/4132/5084588268_0a448b9d35_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/10/15/what-is-the-next-number.html> h4 classmedia-heading>What is the next number?/h4> /a> A classical problem involving ordered lists of numbers. What is the next term in the following sequence? div styletext-align:right; width:100%;> a href/post/2010/10/15/what-is-the-next-number.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-14 itempropdatePublished>October 14, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/14/a-geometric-fallacy.html> img srchttp://farm5.static.flickr.com/4041/5081312425_6ebb5b2376_o_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/10/14/a-geometric-fallacy.html> h4 classmedia-heading>A geometric fallacy/h4> /a> A geometric fallacy is basically a geometric construction that leads to a false result. I once found an obscure russian treatise on this matter (published by мир), that kept me entertained for weeks: Ya.S.Dubnov’s Errores en las demostraciones geométricas. The edition I have is a decent translation into Spanish, m... div styletext-align:right; width:100%;> a href/post/2010/10/14/a-geometric-fallacy.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-10-13 itempropdatePublished>October 13, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/10/13/my-oldest-plays-the-piano.html> img srchttps://farm9.staticflickr.com/8678/15682120759_257ce44a5c_n_d.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2010/10/13/my-oldest-plays-the-piano.html> h4 classmedia-heading>My oldest plays the piano!/h4> /a> Two old friends, Ernie and Bernie, bump into each other in the street. It was more than twenty years since they last saw each other, so they decide to spend some time together in a nearby coffee shop, catching up. At some point, Bernie asks the inevitable: So, you got married? div styletext-align:right; width:100%;> a href/post/2010/10/13/my-oldest-plays-the-piano.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2010-04-28 itempropdatePublished>April 28, 2010/time> /p> div classmedia> a classmedia-left href/post/2010/04/28/the-nonlocal-means-algorithm.html> img srchttps://c1.staticflickr.com/5/4251/34999114475_94fe642e4b_m.jpg stylewidth:75px;> /a> div classmedia-body> a href/post/2010/04/28/the-nonlocal-means-algorithm.html> h4 classmedia-heading>The Nonlocal-means Algorithm/h4> /a> The nonlocal-means algorithm Buades, Coll, Morel was designed to perform noise reduction on digital images, while preserving the main geometrical configurations, as well as finer structures, details and texture. The algorithm is consistent under the condition that one can find many samples of every image detail w... div styletext-align:right; width:100%;> a href/post/2010/04/28/the-nonlocal-means-algorithm.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2008-09-27 itempropdatePublished>September 27, 2008/time> /p> div classmedia> a classmedia-left href/post/2008/09/27/the-hunt-for-a-bellman-function-2.html> img srchttp://farm3.static.flickr.com/2602/4047407579_8397368be9_o.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2008/09/27/the-hunt-for-a-bellman-function-2.html> h4 classmedia-heading>The hunt for a Bellman Function./h4> /a> This is a beautiful and powerful mathematical technique in Harmonic Analysis that allows, among other things, to prove very complicated inequalities in the theory of Singular Integral Operators, without using much of the classical machinery in this field. div styletext-align:right; width:100%;> a href/post/2008/09/27/the-hunt-for-a-bellman-function-2.html> button typebutton classbtn btn-xs btn-default>Read more »/button> /a> /div> /div> /div> p classentry-date date published> time datetime2007-08-05 itempropdatePublished>August 05, 2007/time> /p> div classmedia> a classmedia-left href/post/2007/08/05/mechanical-geometry-theorem-proving.html> img srchttp://farm1.static.flickr.com/113/298203907_77bcce2162.jpg stylewidth:200px;> /a> div classmedia-body> a href/post/2007/08/05/mechanical-geometry-theorem-proving.html> h4 classmedia-heading>Mechanical Geometry Theorem Proving/h4> /a> In 1977, Professor Wen-Tsun Wu succeeded in developing a method of mechanical geometry theorem proving. This method has been applied to prove or even discover hundreds of non-trivial difficult theorems in elementary and differential geometries on a computer in an almost trivial manner. 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