Constant width
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Also named here as reuleaux triangle — the same set of essays touches all of them, so they are one junction rather than several.
Round is not the only way to be the same width
A shape that measures the same in every direction sounds like a description of a circle. It is not — there are infinitely many others, one of them is on a coin in most people's pockets, and a drill built from one cuts a nearly square hole.
The most area a fence can hold
One length of boundary, and the question of what shape to bend it into. The answer is a circle, everybody knows it, and the argument that convinced the nineteenth century turned out to prove something slightly different.
Named alongside it
The objects these essays reach for when they reach for this one.
AreaConvexityReuleaux triangleBarbier's theoremCircleExistence proofIntegral geometryOptimalityPiRegular polygonScalingSupport function