Reality tunnels » mathematics http://blog.superadditive.com A glimpse into my visual space Wed, 16 Dec 2009 09:56:25 +0000 en hourly 1 http://wordpress.org/?v=3.0.1 Applications of the absolute quadratic complex and the quadric of segments in 3D reconstruction. http://blog.superadditive.com/2009/12/16/applications-of-the-absolute-quadratic-complex-and-the-quadric-of-segments-in-3d-reconstruction/ http://blog.superadditive.com/2009/12/16/applications-of-the-absolute-quadratic-complex-and-the-quadric-of-segments-in-3d-reconstruction/#comments Wed, 16 Dec 2009 09:56:25 +0000 jmbr http://blog.superadditive.com/?p=118 The final project in my post-graduate degree in Mathematics explains two approaches for computing a Euclidean upgrading of a projective 3D reconstruction, which has applications in Computer Vision. The slides for a talk I gave a couple of weeks ago explaining the subject matter are also available online.

]]> http://blog.superadditive.com/2009/12/16/applications-of-the-absolute-quadratic-complex-and-the-quadric-of-segments-in-3d-reconstruction/feed/ 0 Introductory talk on Geometric Algebra http://blog.superadditive.com/2009/08/15/introductory-talk-on-geometric-algebra/ http://blog.superadditive.com/2009/08/15/introductory-talk-on-geometric-algebra/#comments Sat, 15 Aug 2009 08:16:37 +0000 jmbr http://blog.superadditive.com/?p=103 A few weeks ago I gave at work an introductory talk on Geometric Algebra. In my slides, I mostly followed the exposition in David Hestenes’ New Foundations for Classical Mechanics. And since we’re mostly a MATLAB shop I also used Gable to show how to perform some practical computations.

]]> http://blog.superadditive.com/2009/08/15/introductory-talk-on-geometric-algebra/feed/ 7 Functional programming in Maple http://blog.superadditive.com/2009/02/09/functional-programming-in-maple/ http://blog.superadditive.com/2009/02/09/functional-programming-in-maple/#comments Mon, 09 Feb 2009 20:45:59 +0000 jmbr http://blog.superadditive.com/?p=92 I have written some notes on functional programming in Maple mainly to help me find my way around. For the moment they’re terse but I might expand them.

]]> http://blog.superadditive.com/2009/02/09/functional-programming-in-maple/feed/ 0 Planet Sage http://blog.superadditive.com/2007/12/13/planet-sage/ http://blog.superadditive.com/2007/12/13/planet-sage/#comments Thu, 13 Dec 2007 10:58:06 +0000 jmbr http://blog.superadditive.com/2007/12/13/planet-sage/ There’s a new blog aggregator dedicated to Sage, it is Planet Sage. Enjoy!

]]> http://blog.superadditive.com/2007/12/13/planet-sage/feed/ 0 cl-buchberger is out! http://blog.superadditive.com/2007/10/19/cl-buchberger-is-out/ http://blog.superadditive.com/2007/10/19/cl-buchberger-is-out/#comments Fri, 19 Oct 2007 18:36:10 +0000 jmbr http://blog.superadditive.com/2007/10/19/cl-buchberger-is-out/ I’ve just released the first version of cl-buchberger, a Common Lisp
implementation of Buchberger’s algorithm for the computation of
Gröbner bases.

There are many improvements waiting in the pipeline but the basic
functionality is there.

Lisp logo

You can read more about cl-buchberger here.

]]> http://blog.superadditive.com/2007/10/19/cl-buchberger-is-out/feed/ 0 Mathematics, cryptography, and the real world http://blog.superadditive.com/2007/09/06/mathematics-cryptography-and-the-real-world/ http://blog.superadditive.com/2007/09/06/mathematics-cryptography-and-the-real-world/#comments Thu, 06 Sep 2007 20:28:33 +0000 jmbr http://blog.superadditive.com/2007/09/06/mathematics-cryptography-and-the-real-world/ Among the many reactions to Neil Koblitz’ article on modern cryptography in the Notices of the AMS the most interesting reply I’ve read is this one by Steven Bellovin:

Mathematicians have known since Euclid that axioms are important.
Security, though, is math embedded in the real world, and that
matters. Put another way, Euclidean geometry is completely valid as a
pure mathematical system. But that doesn’t mean it applies in a
relativistic universe. Sure, we live far from any space-warping
masses, so we can pretend that the angles in our triangles add up to
180 degrees. In the security world, though, the attacker will toss a
black hole at us to warp the space around our provably-secure
triangular encryptor. Was that proof of security flawed? Ask Riemann
or Lobachevsky.

]]> http://blog.superadditive.com/2007/09/06/mathematics-cryptography-and-the-real-world/feed/ 1 Short films on topology http://blog.superadditive.com/2007/07/12/short-films-on-topology/ http://blog.superadditive.com/2007/07/12/short-films-on-topology/#comments Thu, 12 Jul 2007 14:38:06 +0000 jmbr http://blog.superadditive.com/2007/07/12/short-films-on-topology/ Youtube user bothmer has posted a collection of nifty films related to topology and algebraic geometry. As an appetizer, I leave you with this one on Compactness and the Stereographic Projection:

You can find more movies at Advent Calendar 2006 – Geometrical Animations.

]]> http://blog.superadditive.com/2007/07/12/short-films-on-topology/feed/ 0 The Mathematical Cartoons of Larry Gonick http://blog.superadditive.com/2007/05/19/the-mathematical-cartoons-of-larry-gonick/ http://blog.superadditive.com/2007/05/19/the-mathematical-cartoons-of-larry-gonick/#comments Sat, 19 May 2007 22:59:42 +0000 jmbr http://blog.superadditive.com/2007/05/19/the-mathematical-cartoons-of-larry-gonick/ xkcd‘s latest comic strip reminded me of this page where you can read some of Larry Gonick’s mathematics-centered comics. I discovered this artist through his book The Cartoon Guide to Statistics which might not be the most thorough text on the subject but it surely is the funniest.
Seymour, cloak-and-dagger mathematician

]]> http://blog.superadditive.com/2007/05/19/the-mathematical-cartoons-of-larry-gonick/feed/ 2 Separation axioms and the Topology Database http://blog.superadditive.com/2007/03/15/separation-axioms-and-the-topology-database/ http://blog.superadditive.com/2007/03/15/separation-axioms-and-the-topology-database/#comments Thu, 15 Mar 2007 22:42:46 +0000 jmbr http://blog.superadditive.com/2007/03/15/separation-axioms-and-the-topology-database/ I recently deemed it convenient to be able to see the relationship between some general topology concepts in Separation axiomsjust one gaze. That’s why I prepared a graph describing their implications. I have made it available here hoping that it will be of use for someone else. All the definitions come from the book General Topology by Stephen Willard.

I needed to roll my own solution but Ryan Dahl has set up the Topology Database and this website not only publishes more implication graphs like the one above but it also intends to be the online equivalent to Counterexamples in Topology. This is a wiki-like site and the author even publishes the source code licensed under the GNU General Public License.

]]> http://blog.superadditive.com/2007/03/15/separation-axioms-and-the-topology-database/feed/ 0 Superficies http://blog.superadditive.com/2006/12/24/superficies/ http://blog.superadditive.com/2006/12/24/superficies/#comments Sun, 24 Dec 2006 09:36:14 +0000 jmbr http://blog.superadditive.com/2006/12/24/superficies/ I recently came across Superficies, a very nice tool for exploring surfaces and differential geometry concepts that I wanted to share. Here’s a link to its english manual that will give you an idea of the program’s features.

A monkey's saddle in Superficies

This is GPLed software written in Delphi and although binaries are only available for Windows I had no problem running it under Linux using Wine.

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