Using design to develop an in-depth understanding of mathematical surfaces: The hairy Klein bottle.

The Klein bottle and hairy ball theorem are important concepts in advanced mathematics and they are both examples of the Poincaré–Hopf theorem. Complex theories such as these usually remain unrealized in the minds of mathematicians. In this collaborative work between a mathematician and a designer, we introduce the concept of the hairy Klein bottle, which is a fusion that explores a continuous non-vanishing vector field on a non-orientable surface. We strive to explain and shape these esoteric concepts accurately and to and describe the modelling process of creating a tangible, touchable sculpture designed to intrigue and invite simple understanding. [ABSTRACT FROM AUTHOR]