Leon Bankoff (December 13, 1908 – February 16, 1997), born in

New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...

New York New York most commonly refers to: * New York City, the most populous city in the United States, located in the state of New York * New York (state), a state in the northeastern United States New York may also refer to: Film and television * '' ...

, was an American

dentist A dentist, also known as a dental surgeon, is a health care professional who specializes in dentistry (the diagnosis, prevention, management, and treatment of diseases and conditions of the mouth, oral cavity and other aspects of the craniofaci ...

. As an amateur mathematician he constructed the

Bankoff circle In geometry, the Bankoff circle or Bankoff triplet circle is a certain Archimedean circle that can be constructed from an arbelos; an Archimedean circle is any circle with area equal to each of Archimedes' twin circles. The Bankoff circle was firs ...

. He was also an

Esperantist An Esperantist ( eo, esperantisto) is a person who speaks, reads or writes Esperanto. According to the Declaration of Boulogne, a document agreed upon at the first World Esperanto Congress in 1905, an Esperantist is someone who speaks Esperanto ...

Life

After a visit to the

City College of New York The City College of the City University of New York (also known as the City College of New York, or simply City College or CCNY) is a public university within the City University of New York (CUNY) system in New York City. Founded in 1847, Cit ...

, Bankoff studied dentistry at

New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the ...

. Later, he moved to

Los Angeles Los Angeles ( ; es, Los Ángeles, link=no , ), often referred to by its initials L.A., is the largest city in the state of California and the second most populous city in the United States after New York City, as well as one of the world' ...

California California is a U.S. state, state in the Western United States, located along the West Coast of the United States, Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the List of states and territori ...

, where he taught at the

University of Southern California The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in C ...

; while there, he completed his studies. He practiced over 60 years as a dentist in

Beverly Hills Beverly Hills is a city located in Los Angeles County, California. A notable and historic suburb of Greater Los Angeles, it is in a wealthy area immediately southwest of the Hollywood Hills, approximately northwest of downtown Los Angeles. Bev ...

. Many of his patients were celebrities. Along with Bankoff's interest in dentistry were the

piano The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboa ...

and the

guitar The guitar is a fretted musical instrument that typically has six strings. It is usually held flat against the player's body and played by strumming or plucking the strings with the dominant hand, while simultaneously pressing selected stri ...

. He was fluent in

Esperanto Esperanto ( or ) is the world's most widely spoken constructed international auxiliary language. Created by the Warsaw-based ophthalmologist L. L. Zamenhof in 1887, it was intended to be a universal second language for international communi ...

, created artistic sculptures, and was interested in the progressive development of computer technology. Above all, he was a specialist in the mathematical world and highly respected as an expert in the field of flat geometry. Since the 1940s, he lectured and published many articles as a co-author. Bankoff collaborated with

Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...

in a mathematics paper and therefore has an Erdős number 1. From 1968 to 1981, Bankoff was the editor of the ''Problem Department'' of

Pi Mu Epsilon Pi Mu Epsilon ( or ) is the U.S. honorary national mathematics society. The society was founded at Syracuse University on , by Professor Edward Drake Roe, Jr, and currently has chapters at 371 institutions across the US. Goals Pi Mu Epsilon is d ...

Journals, where he was responsible for the publication of some 300 top problems in the area of

plane geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms ...

, particularly

Morley's trisector theorem In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle. The theorem ...

, and the

arbelos In geometry, an arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others (connected), all on the same side of a straight line (the ''baseline'') that conta ...

Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists ...

. Among his discoveries with the arbelos was the

, which is equal in area to

Archimedes' twin circles In geometry, the twin circles are two special circles associated with an arbelos. An arbelos is determined by three collinear points , , and , and is the curvilinear triangular region between the three semicircles that have , , and as their diame ...

Publications

* ''How Did Pappus Do It?'' The Mathematical Gardner,

David A. Klarner David Anthony Klarner (October 10, 1940March 20, 1999) was an American mathematician, author, and educator. He is known for his work in combinatorial enumeration, polyominoes, and box-packing.Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...

and Murray S. Klamkin) Mathematics Magazine, 46 (1973), 270-272.

References

* Donald J. Albers &

Gerald L. Alexanderson Gerald Lee Alexanderson (1933–2020) was an American mathematician. He was the Michael & Elizabeth Valeriote Professor of Science at Santa Clara University, and in 1997–1998 was president of the Mathematical Association of America. He was also ...

(2011) ''Fascinating Mathematical People: interviews and memoirs'', "Leon Bankoff", pp. 79–95,

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial su ...

, . {{DEFAULTSORT:Bankoff, Leon 20th-century American mathematicians Geometers American Esperantists 1908 births 1997 deaths