In the ‘Wild West’ of Geometry, Mathematicians Redefine the Sphere

If you’ve ever been stuck in traffic on a rainy afternoon, you’ve probably watched raindrops racing each other down the car window. When pairs of droplets collide, they merge into a new droplet, losing their separate identities. That merging is possible because the water droplets are just about spherical. When shapes are flexible — as raindrops are — attaching a sphere doesn’t change anything.

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