ABSTRACT
This chapter begins with an exploration of the iconic picture by Salvador Dalí of melting clocks and a picture of a man stretching and unwinding as he falls into a black hole, both examples of topology in art. Topology is defined in terms of topological transformations—stretching and shrinking without tearing or pasting. The first example of topology, the Königsberg bridge problem, is explained; the solution using an abstract representation of the bridges and land masses is given. The classic example of a coffee cup transformed into a donut is explained. The cylinder and Möbius band are constructed, and their properties are compared. The Klein bottle is discussed. The final section gives examples of how artists use topology. The chapter concludes with a list of exercises, readings, and artists who use topology.
