Why Triangles are Easy and Tetrahedra are Hard — Quanta Magazine

My latest column for Quanta Magazine is a celebration of the Triangle Angle Sum theorem, a favorite result from high school geometry.

Do you think there’s a triangle whose angles measure 41, 76 and 63 degrees?

At first, answering this may seem easy. From geometry class we know that the sum of the measures of the interior angles of a triangle is 180 degrees, and since 41 + 76 + 63 = 180, the answer must be yes.

But there’s more to this question than meets the eye.

From triangles we move to tetrahedra, where a surprisingly simple question about angles wasn’t resolved until 2020. You can read all about it here.