Arthur Preston Mellish
Arthur Preston Mellish 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
- a curve is of constant width;
- a curve is of constant diameter;
- all the normals of a curve are double;
- the sum of radii of curvature at opposite points of a curve is constant;
are equivalent, in the sense that whenever one of statements is true, all other statements also hold.
- All curves of the same width a have the same length L given by L = a.
