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Physical models of abstract math: How Round Is Your Circle?

How Round Is Your Circle? This abstract math video shares a series of visual examples of how physical models are created from abstract mathematical ones. They’re from a book called How Round Is Your Circle?, written by John Bryant and Chris Sangwin.

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

Dudeney's Dissection
Chebyshev's linkage
Video examples include: Sarrus’ mechanism, slotted ellipses, slotted disks, super egg, two-tip tetrahedron, Conway and Guy’s unistable polyhedron, solids of constant width, drilling a square hole, Dudeney’s Dissection, Chebyshev’s linkage, Peaucellier’s linkage, and Hart’s straight-line linkage and A-frame,

We liked watching all of these abstract math examples, but Dudeney’s Dissection — cutting an equilateral triangle into pieces which can be rearranged into a square via well-placed hinges — is a favorite, as are solids of constant width, which we received as a gift from the team at Maths Gear.

Related: Straight line mechanism and more about abstract math.

Next: Hypocycloid circular motion optical illusion, The Graceful Tree Problem, The Sphere-Packing Problem, and an accidental toy inventor’s shapeshifting designs.

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