George Odom

George Phillips Odom, Jr ( 1941 - December 18, 2010) is an American artist and amateur geometer best known for his contributions to the golden ratio (Φ).

life and work

In the 1960s, Odom was first known in New York for his fiber optic alternators, which he exhibited in the Knoll International Gallery in Manhattan. Odom suffered from depression that later culminated in a suicide attempt and eventually led to him living largely isolated from the outside world at the Hudson River Psychiatric Center in Poughkeepsie since the early 1980s .

Problem E2007 (Odom, 1983)

{\ displaystyle {\ tfrac {| AB |} {| BC |}} = {\ tfrac {| AC |} {| AB |}} = \ Phi}

Odom's interest in geometry was sparked by visiting an exhibition by Buckminster Fuller in the 1960s. In the mid-1970s he wrote to the Canadian geometer Donald Coxeter , because he was of the opinion that his artistic work would also be of a certain interest from a mathematical point of view. A regular correspondence then developed with Coxeter and another mathematician, the Benedictine monk Father Magnus Wenniger from Minnesota , which would last for over 25 years. The two mathematicians thus became one of the few regular contacts with the outside world that Odom has had since living at the Hudson River Psychiatric Center . He corresponded with them not only about mathematics, but also about psychology, philosophy, religion and world events. In mathematics, he was interested in geometric figures and the golden ratio. He discovered several previously unknown examples of the appearance of the golden ratio in various elementary geometric figures. The two mathematicians passed on Odom's findings and suggestions in their lectures and discussions, and Coxeter also processed them in several publications. The best known is the construction of the golden section with the help of an equilateral triangle and its circumference . Using this construction, Coxeter formulated a problem that was published in 1983 as Problem E3007 in the American Mathematical Monthly :

Let A and B be the center of the sides EF and ED of the equilateral triangle DEF. Extend AB so that the extension intersects the perimeter of the triangle DEF in C. Now show that B divides AC in the golden ratio .

{\ displaystyle {\ tfrac {| AE |} {| AF |}} = {\ tfrac {| EF |} {| AE |}} = \ Phi}

Odom found another way to construct the golden ratio using an equilateral triangle:

Given is an equilateral triangle ABC with the height from C to AB. Let D be the base of the height. Now you extend the height above D by the length of the distance BD. Let E be the end point of the extension. Now you connect the points E and A and extend this distance beyond A so that it forms the circle around D with the radius | CD | intersects in F. A now divides the line EF in the golden ratio.

{\ displaystyle {\ tfrac {| AC |} {| AB |}} = {\ tfrac {| AB |} {| BC |}} = \ Phi}

Odom dealt with models and sculptures, which were composed of 3-dimensional geometric figures, and also examined the occurrence of golden sections there. In doing so, he discovered two simple examples of its occurrence in Platonic solids , namely in the tetrahedron and in the cube . If you connect the side centers of a triangular surface of a tetrahedron and extend this line so that it intersects the sphere of the tetrahedron, then the three points form a line that is divided in the golden ratio. If you cut open the sphere along the plane in which the triangular surface with the side centers lies, the configuration of exercise E3007 results in this plane. If you connect the middle of any two adjacent surfaces of a cube and extend the line so that it intersects the cube's sphere at one point, then this point, together with the two side centers, also forms a line that is divided in the golden ratio.

When Wenniger informed him of Coxeter's death in 2003, Odom said, “I don't know what I would have done without you, Socantens [his doctor] and Coxeter. You three were my only contact with humanity. "

In 2007 Odom was visited by Princeton mathematician John Horton Conway in Poughkeepsie.

literature

Siobhan Roberts: Cubic Connection . In: The Walrus , April 2007
Siobhan Roberts: A Reclusive Artist Meets Minds with a World-Famous Geometer: George Odom and HSM (Donald) Coxeter . Leonardo, Volume 40, No. 2, 2007, pp. 175-177 ( JSTOR )
Doris Schattschneider : Coxeter and the Artists: Two-way Inspiration . In: Harold Scott Macdonald Coxeter (Ed.), Chandler Davis (Ed.), Erich W. Ellers (Ed.): The Coxeter Legacy: Reflections and Projections . AMS , 2006, ISBN 0-8218-3722-2 , pp. 255–280, here pp. 268–270 ( excerpt from Google book search)

Web links

Pat Ballew: The Geometric Beauty of a Troubled Mind
Golden Ratio in Equilateral Triangle on the Shoulders of George Odom on cut-the-knot.org

Individual evidence

^ Siobhan Roberts: Genius At Play: The Curious Mind of John Horton Conway . Bloomsbury Publishing USA, 2015, ISBN 9781620405949 , p. 440
^ ^A ^b ^c Siobhan Roberts: Cubic Connection . In: The Walrus , April 2007
↑ ^a ^b ^c ^d ^e ^f Doris Schattschneider : Coxeter and the Artists: Two-way Inspiration . In: Harold Scott Macdonald Coxeter (Ed.), Chandler Davis (Ed.), Erich W. Ellers (Ed.): The Coxeter Legacy: Reflections and Projections . AMS , 2006, ISBN 0-8218-3722-2 , pp. 255–280, here pp. 268–270 ( excerpt from Google book search)

personal data
SURNAME	Odom, George
ALTERNATIVE NAMES	Odom, George Phillips (full name)
BRIEF DESCRIPTION	American artist and amateur surveyor
DATE OF BIRTH	1941
DATE OF DEATH	December 18, 2010

[1] Siobhan Roberts: Genius At Play: The Curious Mind of John Horton Conway . Bloomsbury Publishing USA, 2015, ISBN 9781620405949 , p. 440

[roberts-2] A ^b ^c Siobhan Roberts: Cubic Connection . In: The Walrus , April 2007

[schattschneider-3] ↑ ^a ^b ^c ^d ^e ^f Doris Schattschneider : Coxeter and the Artists: Two-way Inspiration . In: Harold Scott Macdonald Coxeter (Ed.), Chandler Davis (Ed.), Erich W. Ellers (Ed.): The Coxeter Legacy: Reflections and Projections . AMS , 2006, ISBN 0-8218-3722-2 , pp. 255–280, here pp. 268–270 ( excerpt from Google book search)