Vol. 110, No. 1, 1984

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ISSN: 0030-8730
Remarks on Fenn’s “the table theorem” and Zaks’ “the chair theorem”

Mark D. Meyerson

Vol. 110 (1984), No. 1, 167–169
Abstract

In 1970 Roger Fenn showed that one could always balance a square table on a hill. Soon after, Joseph Zaks stated that one can always translate a triangular chair to balance on a hill. Recent results have been found by E. H. Kronheimer and P. B. Kronheimer. This paper gives precise statements of the theorems and shows that:

  1. Compact support for the hill in the Chair Theorem cannot be replaced by lim|x|→∞f(x) = 0 (answering a question of Zaks).
  2. The isometry of the Table cannot be replaced by a translation.
  3. The square Table cannot be replaced by an n-gon table for n 5.
  4. The Table Theorem is still open for cyclic quadrilaterals.

Mathematical Subject Classification 2000
Primary: 52A10
Secondary: 55M20
Milestones
Received: 8 January 1982
Revised: 2 March 1982
Published: 1 January 1984
Authors
Mark D. Meyerson