History

trisectrix in an effort to solve one of the geometric problems of antiquity: that of trisecting an arbitrary angle. The Greeks sought to trisect an angle using only a compass and unmarked straight edge; however, in 1835 Wantzel proved this was impossible.[7] That is not to say it is altogether impossible to trisect any angle—on the contrary, there are many ways to go about it.[2] There are, however, many individuals who claim to have trisected an angle when they find an approximation and do not see any reason for proving their assertion with mathematical rigor. For many practical applications that’s just fine, but any mathematician worth his or her salt knows better than to assume that a result is correct just because it seems to be correct. Maclaurin was certainly a worthy mathematician, and as we will see, he discovered a nice little method for precisely trisecting angles. Before we jump into the mathematics of the Maclaurin trisectrix, there are a few things to be said of Mr. Maclaurin. He was born in Kilmodan, Scotland in 1698. By the time he was ten years old, both of his parents had died and his uncle Daniel Maclaurin was charged with his upbringing. Maclaurin excelled as a student and entered the University of Glasgow at the age of 11 and received his M.A. when he was 14. At 19, he was elected for professorship at Marischal College in the University of Aberdeen.[5] For this Maclaurin reportedly held a world record as the youngest professor until April 2008.[4] He met Isaac Newton in 1719 on a trip to London and later wrote a two-volume work entitled A Treatise on Fluxions (1742) wherein he defended Newton’s calculus.[3][5] Other significant publications by Maclaurin include Geometria Organica (1720), A Treatise of Algebra (1748), and An Account of Sir Isaac Newton’s Philosophy (1748).[6] Maclaurin spent most of his life a bachelor until he married Anne Stewart in 1725, with whom he had seven children. Maclaurin died of dropsy on the June 14th, 1746. Two of his aforementioned works were published posthumously. He is best remembered today for his work on the special Taylor Series centered about zero that bears his name.[5] Equations of the Maclaurin Trisectrix With the asymptote at x = a, origin at crunod