On Wednesday, 16th October, one of our members, inspired by the national U3A science seminar which some of us attended in August, gave us an introduction to “Different Worlds, Different Geometries”.
She started with what we, in the good company of the ancient Babylonians and the ancient Greeks, knew to be always true:
- That the angles of a triangle have to add up to 180 degrees
- That parallel lines can never meet
- That any straight line can be extended as far as you like and it will never meet itself coming back
She then stood us all on our heads (not literally!) by showing us some geometric systems where
- The angles of a triangle can add up to more than 180 degrees, or less
- Parallel lines (e.g. lines of longitude) meet each other more than once
- A straight line can meet itself (think of a line of latitude circling the Earth)
This led on to considering different kinds of map projection, Mercator, Peters and others, and to thinking about what Einstein meant when he said that space is curved. (Curved which way? Somebody said “Every way at once.” What do you think?)
Finally she showed us some of the work of the Dutch artist M. C. Escher, who used some of these unfamiliar geometries in constructing his wonderful tiling patterns.