## Tuesday, 19 January 2016

### The Man Who Named the Nine Point Circle and more

I was doing some biographical notes on the French mathematician, Olry Terquem, recently and realized that for most of the years I taught HS math, I didn't know who he was or what he had done. You neither? Ok, there are lots of little known mathematicians out there and nobody can keep up with all of them, but this guy did a lot of things that might pop up in a HS geometry or analysis class.

I had spent a lot of my career seeking out the origin of the terms in mathematics, so I figured if I didn't know, perhaps a short blog to introduce him, and his work, to the teaching masses out there was in order.... so here goes.

If you teach or talk about the Nine-Point circle, you have Olry to thank for the name. In 1842 he used "le cercle des nevf points", and before that, it had had no actual name. It had been written about in various forms since an 1804 article by Bevin, but many of the writers referred to various aspects of the circle and may not have known it had the qualities others had spoken of. Since then, although it now goes by  a whole bunch of names, six-point circle, twelve-point circle, n-point circle, Fuerbach's Circle, the medioscribed circle, the mid-circle, the circum mid-circle, and Terqeum's circle. Oh, and even Euler's circle sometimes, although Euler never wrote of it.

If you teach, or study, the history of math, you should be aware that the first journal ever dedicated to the history of  mathematics was founded by Terquem in 1851. Terquem and Camille-Christophe Gerono had founded the Nouvelles Annales de MathÃ©matiques in 1842. In 1855 Terquem also founded the Bulletin de Bibliographie, d'Histoire et de Biographie de MathÃ©matiques, which was published as a supplement to the Nouvelles Annales.

And if your mathematical taste goes just a little higher than traditional high school math, it is Terquem who coined the term "Pedal Curve" for the types of curves that Colin MacLaurin introduced in 1718. He also introduced the concept of counting the number of perpendicular lines from a point to an algebraic curve as a function of the degree of the curve. From this approach he also became the first to discover how frequently the minimum or maximum value of a symmetric function is obtained by setting all variables equal to each other.