Leon Bankoff

Leon Bankoff (born December 13, 1908 in New York City , † February 16, 1997 in Los Angeles ) was an American dentist and mathematician .

Life

After attending the City College of New York , Bankoff studied dentistry at New York University ; he later moved to Los Angeles, California , where he completed his studies at the University of Southern California . He practiced as a dentist in Beverly Hills, Los Angeles for over 60 years ; numerous Hollywood celebrities were among his patients.

His interest was by no means limited to dentistry: he spoke fluent Esperanto , played the piano and guitar, created artistic sculptures and was interested in the advancing development of computer technology - but above all he was a highly respected expert in the field of plane geometry in the mathematical world and counted the most important mathematicians of his time among his friends. He gave lectures and published numerous specialist articles from the 1940s onwards. As a co-author of Paul Erdős , Bankoff had the Erdős number  1 (see also the list of specialist articles).

From 1968 to 1981 Bankoff was editor of the Problem Department of the Pi Mu Epsilon Journal , where he was responsible for the publication of around 300 high-profile problems in the field of planar geometry.

The Arbelos (black) with the twin circles of Archimedes (light gray) and Bankoff's third circle (blue). Orange: the inscribed circle of the Arbelos

He was particularly passionate about the Arbelos , a geometrical figure with amazing properties, which Archimedes was probably first investigated. More than 2000 years after Archimedes discovered the twin circles in the Arbelos , Bankoff was able to prove a third circle congruent to the twin circles in 1954 and a fourth one in 1974 - the Bankoff circles later named after him . He published his discoveries in 1974 in a highly regarded article and thus inspired other mathematicians and those interested in mathematics who discovered dozens of other Archimedean circles over the course of the next 30 years .

After leaving his dental practice, Bankoff began work on a comprehensive book on the Arbelos, based a. a. based on material from Victor Thébault (1882–1960), a French mathematician. He could not finish his manuscript - in 1997 he died of cancer.

See also

Bankoff dealt u. a. with the following geometric figures, which he made a significant contribution to researching (see list of specialist articles):

• Morley triangle
• Arbelos with the twin circles
• Butterfly set

swell

1. ↑ List of people with Erdős number 1 on the Erdős Number Project website .
2. ↑ Leon Bankoff: Are the twin circles of Archimedes really twins? In: Mathematics Magazine . MAA 1974. Vol. 47, no. 4: 214-218.
3. ^ Clayton W. Dodge, Thomas Schoch, Peter Y. Woo, Paul Yiu: Those Ubiquitous Archimedean Circles. In: Mathematics Magazine. MAA 1999, No. 72, 202–213 ( facsimile see web links).

literature

• Donald J. Albers, Gerald L. Alexanderson: Fascinating Mathematical People: Interviews and Memoirs. Princeton University Press 2011.

Professional article (selection)

• 1954 about the Arbelos :
  Leon Bankoff: A Mere Coincidence. In: Mathematics Newsletter. Los Angeles City College 1954; reprinted in College Math. Journal 1992, no. 23, 106.
• 1962 on the Morley Triangle :
  Leon Bankoff: A Simple Proof of the Morley Theorem. In: Mathematics Magazine. MAA 1962, Vol. 35, No. 4th, 223-224.
• 1973 about the "asymmetric propeller" (as a co-author of Paul Erdős , Bankoff has the Erdős number 1):
  Leon Bankoff, Paul Erdős, Murray Klamkin: The asymmetric propeller. In: Mathematics Magazine. MAA 1973. No. 46, 270-272.
• 1974 on the twin circles of Archimedes:
  Leon Bankoff: Are the twin circles of Archimedes really twins? In: Mathematics Magazine. MAA 1974. Vol. 47, no. 4: 214-218.
• 1987 on the butterfly theorem :
  Leon Bankoff: The Metamorphosis of the Butterfly Problem. In: Mathematics Magazine. MAA 1987, Vol 60, No. 4, 195-210.
• 1994 about the Arbelos:
  Leon Bankoff: The Marvelous Arbelos. In: The Lighter Side of Mathematics. MAA 1994, 247-253.

Web links

All sources given here are in English.

• In Memoriam - Leon Bankoff (PDF)
• Those Ubiquitous Archimedean Circles (PDF, see sources; 895 kB)
• Leon Bankoff's Surprises
• On Propellers from Triangles (PDF file; 171 kB)