Leon Bankoff born in New York City

New York City

New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...

, New York

New York

New York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east...

, was an American

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 dentist

Dentist

A dentist, also known as a 'dental surgeon', is a doctor that specializes in the diagnosis, prevention, and treatment of diseases and conditions of the oral cavity. The dentist's supporting team aides in providing oral health services...

 and mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

.

Life

After a visit to the City College of New York

City College of New York

The City College of the City University of New York is a senior college of the City University of New York , in New York City. It is also the oldest of the City University's twenty-three institutions of higher learning...

, Bankoff studied dentistry at New York University

New York University

New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...

. Later, he moved to Los Angeles

Los Ángeles

Los Ángeles is the capital of the province of Biobío, in the commune of the same name, in Region VIII , in the center-south of Chile. It is located between the Laja and Biobío rivers. The population is 123,445 inhabitants...

, California

California

California is a state located on the West Coast of the United States. It is by far the most populous U.S. state, and the third-largest by land area...

, where he taught at the University of Southern California

University of Southern California

The University of Southern California is a private, not-for-profit, nonsectarian, research university located in Los Angeles, California, United States. USC was founded in 1880, making it California's oldest private research university...

; while there, he completed his studies. He practiced over 60 years as a dentist in Beverly Hills. Among many of his patients were celebrities.

Along with Bankoff's interest in dentistry were the piano

Piano

The piano is a musical instrument played by means of a keyboard. It is one of the most popular instruments in the world. Widely used in classical and jazz music for solo performances, ensemble use, chamber music and accompaniment, the piano is also very popular as an aid to composing and rehearsal...

 and the guitar

Guitar

The guitar is a plucked string instrument, usually played with fingers or a pick. The guitar consists of a body with a rigid neck to which the strings, generally six in number, are attached. Guitars are traditionally constructed of various woods and strung with animal gut or, more recently, with...

. He spoke fluent in Esperanto

Esperanto

is the most widely spoken constructed international auxiliary language. Its name derives from Doktoro Esperanto , the pseudonym under which L. L. Zamenhof published the first book detailing Esperanto, the Unua Libro, in 1887...

, 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

Flat (geometry)

In geometry, a flat is a subset of n-dimensional space that is congruent to a Euclidean space of lower dimension. The flats in two-dimensional space are points and lines, and the flats in three-dimensional space are points, lines, and planes....

. Since the 1940s, he lectured and published many articles as a co-author. Bankoff collaborated with Paul Erdős

Paul Erdos

Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...

 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

Pi Mu Epsilon is the U.S. honorary national mathematics society.The society was founded at Syracuse University on May 25, 1914, by Professor Edward Drake Roe, Jr, and currently has chapters at 337 institutions across the nation.-Goals:...

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

Euclidean geometry

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...

, particularly Morley's trisector theorem

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 Morley triangle. The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley...

, and the arbelos

Arbelos

In geometry, an arbelos is a plane region bounded by a semicircle of diameter 1, connected to semicircles of diameters r and , all oriented the same way and sharing a common baseline. Archimedes is believed to be the first mathematician to study its mathematical properties, as it appears in...

 of Archimedes

Archimedes

Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...

. Among his discoveries with the arbelos was the Bankoff circle

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 first constructed by Leon Bankoff.-Construction:The...

, which is equal in area to Archimedes' twin circles.

Publications

• How Did Pappus Do It? The Mathematical Gardner, David Klarner ed. (Pridle, Weber & Schmidt, 1981).
• The Metamorphosis of the Butterfly Theorem, Mathematics Magazine, Mathematical Association of America, October 1987.
• "The Asymmetric Propeller," (with Paul Erdős
  Paul Erdos
  Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
  
   and Murray S. Klamkin
  Murray S. Klamkin
  -Life:He was born on March 5, 1921 in Brooklyn, New York.He received a bachelor's degree from the Cooper Union in 1942 and a master's from the Polytechnic Institute of Brooklyn in 1947, where he taught from 1948 until 1957. After this Klamkin worked at AVCO, taught at SUNY Buffalo , and worked on...
  
  ) Mathematics Magazine, 46 (1973), 270-272.