4nomore.net » mathematics

Moebius Transformations Visualized

admin — Mon, 03 Mar 2008 20:22:00 +0000

Nicely illustrative video Mobius Transformations Revealed, done by Douglas N. Arnold and Jonathan Rogness of the University of Minnesota in Minneapolis.

Avidan Shamir: Seam Carving For Content Aware Image Resizing

admin — Thu, 13 Sep 2007 21:06:00 +0000

A really cool and beautiful idea, how one can resize images in a content-aware fashion – check the picture for (ragged) lines across the picture which provide the lowest additional details to the picture.
The video is giving a very good impression!
Nice idea – nice result!

Shai Avidan, Ariel Shamir: Seam Carving for Content-Aware Image Resizing
ACM Transactions on Graphics, Volume 26, Number 3,
SIGGRAPH 2007

Paper: http://www.faculty.idc.ac.il/arik/imret.pdf
Video (high-res): http://www.faculty.idc.ac.il/arik/IMRet-All.mov
Video (low-res): http://www.youtube.com/watch?v=vIFCV2spKtg

Eschers Print Gallery: Filled

admin — Sun, 06 Aug 2006 14:25:00 +0000

Very nice work and article how to fill the white space in Eschers Print Gallery: http://escherdroste.math.leidenuniv.nl

The filled version can be found at http://escherdroste.math.leidenuniv.nl/index.php?menu=im&sub=main&view=1.

Rebecca Goldstein: Gödel and the nature of mathematical truth

admin — Fri, 26 Aug 2005 00:27:00 +0000

Insightful article – new for me that Gödels incompleteness theorem actually makes a point for a mathematical reality outside of human environment (since it shows that there are true statements, which cannot formally proved).
Also interesting that therefore the effect his finding had is kind of contrary to what he wanted to achieve.

“Gödel was a mathematical realist, Platonist. … Platonism isn’t a mathematical theorem at all. Of course, Gödel made it harder not to be a Platonist.”

Article is online at Edge 162.