Vol. 110, No. 1, 1984

Recent Issues
Vol. 330: 1
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Remarks on Fenn’s “the table theorem” and Zaks’ “the chair theorem”

Mark D. Meyerson

Vol. 110 (1984), No. 1, 167–169

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
Received: 8 January 1982
Revised: 2 March 1982
Published: 1 January 1984
Mark D. Meyerson