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→Generalizations: Delta curves of height ''h'' all share the same perimeter, {{math|2π''h''/3}}.<ref name="CRC"/> |
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Famous examples of a curve of constant width are the British [[British coin Twenty Pence|20p]] and [[British coin Fifty Pence|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 is true of the 11-sided [[loonie]] (Canadian dollar coin).
There exists a polynomial <math>f(x,y)</math> of degree 8, whose graph (i.e., set of points in <math>\R^2</math> for which <math>f(x,y)=0</math>) is a non-circular curve of constant width.<ref>{{cite journal | url = http://www.mathpropress.com/stan/bibliography/polynomialConstantWidth.pdf | title = A Polynomial Curve of Constant Width | first = Stanley | last = Rabinowitz | journal = Missouri Journal of Mathematical Sciences | volume = 9 | date = 1997 | pages = 23–27 }}</ref> Specifically,
:<math>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</math>
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