Four color theorem
Videos
In mathematics, the four color theorem, or the four-color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same c
As they had with Donald Gillies' discovery of the then-largest prime number using ILLIAC II in 1963, the University of Illinois Urbana-Champaign Mathematics department celebrated the discovery of Appel and Haken's computer-aided proof of the Four color theorem by altering their postage meter.
Klein bottle
Videos
In mathematics, the Klein bottle is an example of a surface with no distinct inside or outside. In other words, it is a one-sided surface which, if traveled upon, could be followed back to the point o
Four color theorem
…in 1890 and, after contributions by several people, proved by Gerhard Ringel and J. W. T. Youngs in 1968. The only exception to the formula is the Klein bottle, which has Euler characteristic χ = 0 (hence the formula gives p = 7) but requires only six colors, as shown by Philip Franklin in 1934. For example…
Immersed Klein bottles in the Science Museum in London
A hand-blown Klein bottle
The pinched torus immersion of the Klein bottle