Number Gossip. Imaging maths - Inside the Klein bottle. September 2003 My first practical experience with a Klein bottle was a failure. When I was still at school I came across a picture of a Klein bottle in a weekly journal. I shared my fascination with a friend who was a glassmaker specializing in physics equipment for schools. A few days later I was a proud owner of a physical Klein bottle, made of glass. What to do with such a bottle? To my delight, this primitive but interesting thermometer did indeed show signs of life during the day. The Klein bottle was discovered in 1882 by Felix Klein [1] and since then has joined the gallery of popular mathematical shapes known to the general public outside the "ivory tower".
From the Möbius band to the projective plane The Möbius band is the simplest one-sided surface, and is easy to make out of a strip of paper. The band was discovered in 1858 by the German astronomer and mathematician August Ferdinand Möbius. Despite its simplicity the Möbius band was a genuine mathematical discovery. Felix Klein. HeartCurves_801.gif (455×306) Web Equation.
Hypercube Projection.