Proof that every rational algebraic equation has a root

A short proof that every finite graph has a tree-decomposition displaying its tangles

We give a short proof that every finite graph (or matroid) has a tree-decomposition that displays all maximal tangles. This theorem for graphs is a central result of the graph minors project of Robertson and Seymour and the extension to matroids is due to Geelen, Gerards and Whittle.

New Proof of the Theorem That Every

Which Carl Friedrich Gauss has presented, In order to obtain the highest honors in philosophy, To the famous faculty of philosophers At the Julia Carolina Academy.

Every Body Has a Brain

[1] http://ebhb.morphonix.com/ [2] http://fireflyfoundation.wordpress.com/brain-games/every-body-has-a-brain/ [3] http://dev.cdgr.ucsb.edu/organizations/morphonix [4] http://dev.cdgr.ucsb.edu/category/genre/educational [5] http://dev.cdgr.ucsb.edu/category/genre/music/dance [6] http://dev.cdgr.ucsb.edu/category/topics/anatomy [7] http://dev.cdgr.ucsb.edu/category/topics/brain [8] http://dev.cdg...

Every Algorithm Has a POV

A Simple Proof That Rational Curves on K3 Are Nodal

The Picard group of S is generated by two effective divisors C and F with C = −2, F 2 = 0 and C · F = 1. It can be realized as an elliptic fiberation over P with a unique section C, fibers F and λ = 2. It is the same special K3 surface used by Bryan and Leung in their counting of curves on K3 surfaces [B-L]. It is actually the attempt to understand their method that leads us to our proof. We wi...