# Julio Garavito and the Nine Point Circle Society

Ricardo Lleras Codazzi (1869-1941) was born in BogotÃ¡, Colombia, the son of the engineer and mathematician Luis Lleras Triana and his wife Rosario Codazzi, the daughter of Agostino Codazzi who the famous Italian geographer and cartographer. Lleras Codazzi became was a mining engineer, geologist, mineralogist and naturalist in Colombia. He was a member of Julio Garavito's Nine Point Circle Society and he gave an interesting description of that unusual society in Ricardo Lleras Codazzi, Julio Garavito,

*El Catolicismo*(20 May 1920).**Julio Garavito and the Nine Point Circle Society**

I want to talk about the Nine Point Circle Society which was one of the strangest and most original societies that is known. It was born and took shape during the three years' war. A few mathematical buffs, of a somewhat shy character, some half unsociable and others completely unsociable, began to gravitate around Julio Garavito, attracted by the irresistible force of his intelligence and fascinated by his undeniable superiority, like butterflies around intense light, in the warmth of his affable and easy manner, under the indelible impression of his highly instructive conversation and by the influence of the community of ideas. A kind of club or circle was gradually formed, which very soon had a special ceremony which, by the way, was quite symbolic.

The society in question was designated by the name of the Nine Point Circle Society, as a tribute to the memory of Euler, for the theorem that bears that name; its members were called "points" and could not be more than nine because there are nine cyclical points related to Euler's triangle (the three feet of the perpendiculars, the three feet of the medians and the three Euler points on the altitudes), nor could they be less than three because three points, not situated in a straight line, determine a circle in position and magnitude, for the same reason there was a quorum with only three of the "points".

Libations were made with liquid coffee, of which enormous quantities were consumed. The "points" had to be fond of mathematics and especially passionate about geometry; finally, each one had to give a proof of Euler's theorem. I remember that Julio's proof, which was by far the best of all, was of an analytical nature and he generalised it to the geometry of space with an original theorem, the sphere of twenty-four points on a reference tetrahedron.

... At first, they only discussed about "matters" of mathematics, mainly geometric questions were proposed, but little by little they began to deal with questions of the most intricate philosophy, but of a strange philosophy, essentially mathematical and founded on the principles peculiar to this science. Curious theories emerged such as that of "The Extrahedrons", "The Sinusoid of Human Life" and the "Great Circle", which was later replaced by "The Asymptotic Transformation", originally proposed by Julio. In a word, time passed pleasantly, the ties between the "points" were tightened and a somewhat intellectual life was led in the midst of that hubbub of materialism that threatened to end what little we have of our fight for high ideals. The Circle suffered from the death of Pedro de Francisco, one of the loftiest characters and noblest souls I have known. Later on, Luis JosÃ© Fonseca died, who, although very young, exercised great influence. Today we lose Julio Garavito, the centre of attraction of our small society, an absolutely indispensable "point" for the existence of others; this loss can no longer be repaired; the Circle is dissolved ipso facto; it is as if the symbolic figure of Euler's theorem had been erased from science.

Last Updated March 2022