Arthur Preston Mellish, Date of Birth, Date of Death
TweetArthur Preston Mellish
Canadian mathematician
Date of Birth: 
About Arthur Preston Mellish
- Arthur Preston Mellish (10 June 1905 – 7 February 1930) was a Canadian mathematician, known for his generalization of Barbier's theorem. Arthur Mellish received in 1928 an M.A.
- in mathematics from the University of British Columbia 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 examined his notes on mathematics.
- Jacob Tamarkin prepared a paper based upon the notes and published it in the Annals of Mathematics in 1931.In the statement of the following theorem, an oval means a closed convex curve. Mellish's Theorem: The statements (i) a curve is of constant width; (ii) a curve is of constant diameter; (iii) all the normals 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 = pa.
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