Everyone learns the number one rule about triangles in high school: the angles of a triangle add up to 180 degrees. But did you know that sometimes they don't? Triangles are much more interesting than ...

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One hypothesis about the shape of the universe is that the universe is in the space of Euclidean geometry and flat. In Euclidean geometry, it is assumed that straight lines extend everywhere, planes ...

This media is in the public domain (free of copyright restrictions). You can copy, modify, and distribute this work without contacting the Smithsonian. For more information, visit the Smithsonian's ...

The shortest distance between two points is a straight line. This is one of the basic principles of Euclidean geometry. But we live on a spherical Earth, so we cannot travel the straight line path ...

This paper gives the exact evaluation of the shape density on the shape space Σ (S2,3) for a labelled random spherical triangle whose vertices are i.i.d.-uniform in a 'cap' of S2 bounded by a 'small' ...

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American Most of us learn some amount of Euclidean ...