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A
theorem on partitions of mass-distribution
V. V. Menon |
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Vol. 16 (1966), No. 1, 133–137
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Abstract |
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A ‘bisector’ of a continuous mass-distribution M in a bounded region on the plane is defined as a straight line such that the two half-planes determined by this line contain half the mass of M each. It is known that there exists at least one point (in the plane) through which pass three bisectors of M. Theorem. Let, for a continuous mass distribution M, the point P through which three bisectors pass be unique. Then all bisectors of M pass through p. The following corollary also is established: For a convex figure K (i.e., compact convex set with nonempty interior) to be centrally symmetric, it is necessary and sufficient that the point through which three bisectors of area pass be unique. |
Mathematical Subject Classification
Primary: 52.40
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Milestones
Received: 25 January 1964
Revised: 30 July 1964
Published: 1 January 1966
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Authors |
| V. V. Menon | |
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