Arthur Preston Mellish (10 June 1905 – 7 February 1930) was a
Canadian
Canadians (french: Canadiens) are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many (or all) of these connections exist and are collectively the source of ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
, known for his generalization of
Barbier's theorem
In geometry, Barbier's theorem states that every curve of constant width has perimeter times its width, regardless of its precise shape. This theorem was first published by Joseph-Émile Barbier in 1860.
Examples
The most familiar examples of c ...
.
Arthur Mellish received in 1928 an M.A. in mathematics from the
University of British Columbia
The University of British Columbia (UBC) is a public university, public research university with campuses near Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks a ...
with thesis ''An illustrative example of the ellipsoid pendulum''. He died at age 24 and had no mathematical publications during his lifetime. After his death, his colleagues at
Brown University
Brown University is a private research university in Providence, Rhode Island. Brown is the seventh-oldest institution of higher education in the United States, founded in 1764 as the College in the English Colony of Rhode Island and Providenc ...
examined his notes on mathematics.
Jacob Tamarkin
Jacob David Tamarkin (russian: Я́ков Дави́дович Тама́ркин, ''Yakov Davidovich Tamarkin''; 11 July 1888 – 18 November 1945) was a Russian-American mathematician best known for his work in mathematical analysis.
Biography ...
prepared a paper based upon the notes and published it in the ''
Annals of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.
History
The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the ...
'' in 1931.
In the statement of the following theorem, an
oval
An oval () is a closed curve in a plane which resembles the outline of an egg. The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or ...
means a
closed
Closed may refer to:
Mathematics
* Closure (mathematics), a set, along with operations, for which applying those operations on members always results in a member of the set
* Closed set, a set which contains all its limit points
* Closed interval, ...
convex curve
In geometry, a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going back to Archimedes. Examples of convex curves include the convex polygons, th ...
.
Mellish's Theorem:
normal Normal(s) or The Normal(s) may refer to:
Film and television
* ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson
* ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie
* ''Norma ...
s of a curve (an oval) are double;
* (iv) the sum of radii of curvature at opposite points of a curve (an oval) is constant;
are equivalent, in the sense that whenever one of statements (i–iv) is true, all other statements also hold.
* (v) All curves of the same (constant) width ''a'' have the same length ''L'' given by ''L'' = ''a''.
References
1905 births
1930 deaths
University of British Columbia alumni
Canadian mathematicians
Differential geometers
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