Curve of constant width - Wikipedia, the free encyclopedia

That's exactly what you thought isn't it.Famous examples of a curve of constant width are the British 20p and 50p coins. Their heptagonal shape with curved sides means that the currency detector in an automated coin machine will always measure the same width, no matter which angle it takes its measurement from. The same same is true of the 11-sided loonie (Canadian dollar coin).

There exists a polynomial f(x,y) of degree 8, whose graph (i.e., set of points in R^2 for which f(x,y)=0) is a non-circular curve of constant width.[4] Specifically,

f(x,y)=(x^2 + y^2)^4 - 45(x^2 + y^2)^3 - 41283(x^2 + y^2)^2 + 7950960(x^2 + y^2) + 16(x^2 - 3y^2)^3

+48(x^2 + y^2)(x^2 - 3y^2)^2 + (x^2 - 3y^2)x[16(x^2 + y^2)^2 - 5544(x^2 + y^2) + 266382] - 720^3.

It was probably true of the old Threepenny Bit as well (ah, yes, I remember them well).

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