The most familiar ideas of geometry were inspired by an ancient vision — a vision of the world as flat. From parallel lines that never meet, to the Pythagorean theorem discussed in last week’s column, these are eternal truths about an imaginary place, the two-dimensional landscape of plane geometry. Conceived in India, China, Egypt and Babylonia more than 2,500 years ago, and codified and refined by Euclid and the Greeks, this flat-earth geometry is the main one (and often the only one) being taught in high schools today. But things have changed in the past few millennia. In an era of globalization, Google Earth and transcontinental air travel, all of us should try to learn a little about spherical geometry and its modern generalization, differential geometry. The basic ideas here are only about 200 years old. Pioneered by Carl Friedrich Gauss and Bernhard Riemann, differential geometry underpins such imposing intellectual edifices as Einstein’s general theory of relativity. At its heart, however, are beautiful concepts that can be grasped by anyone who’s ever ridden a bicycle, looked at a globe or stretched a rubber band. And understanding them will help you make sense of a few curiosities you may have noticed in your travels.
more from Steven Strogatz at The Opinionater here.