Giles Persone de Roberval,who played an integral role in finding the area for these curves, is givencredit for the name 'trochoid.' Blane Pascal, who referred tothese curves as 'roulettes', actually offered cash prizes foranyone able to solve the 'problems' of the area and the centerof gravity of these complex shapes. The initial interest seemsto be stemmed from a paper written in 1501 by Charles Bouvelles in an effortto solve the problem of squaring the circle. Mathematicians first became fascinated with thiscurve in the early 16 th century. The hypotrochoid is a prime exampleof an element of mathematics that lies on such an intersection. We are transported to a world that is at once purely logicalin function yet pure beauty in form. When such seemingly distantfacets of academia arrive at such an intersection the results can be simplyenigmatic. Indeed, there must be an avenue where thefree flowing lines of the art world find a crossroads with the analyticalworlds of the equation and the computation.

There are some areas of mathematics that requireus to cast aside our compulsive preoccupation with practicality and allowourselves the luxury of enjoying the pure aesthetic beauty without anyneed for further justification. Its mathematics are exploredfrom the definition to a derivation of the parametric equations. Its asthetic qualities are explored through visualisation and metaphor. Its history is briefly presented throughthe important figures of its conception.

This paper explores the historic, asthetic and mathematicalqualities of the hypotrochoid curve.

Graphmatica equation for hypotrochoids