When we extend the real number line with a point "infinity"=1/0 the result is a much more complex structure called the real projective line RP¹. In fact, RP¹ is more like a plane -- the hyperbolic plane -- than a line.

This example distils some basic ideas of projective geometry, hyperbolic geometry and Klein's doctrine that geometry is the study of transformation groups and their invariants. The talk will also explain when it is legal to divide by zero, and how to view the rational numbers 2-dimensionally.
 

Convenor: Simon Clarke