Remarks on Two Geometric Conjectures of L. Fejes Schoenberg.
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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In previous papers L. Fejes Toth stated two geometric conjectures concerning the limiting behavior of two infinite sequences of convex polygons obtained by certain simple constructions from a given convex polygon. Toth formulated two conjectures to the effect that appropriate affine images of the nth polygons converge to regular polygons. Using the finite Fourier series the results concerning Conjecture 1 are made more precise. It is also shown by a counter-example 6, 8, 10, ... of sides. However, Conjecture 2 may yet be true for an odd number 5, 7, 9, ... of sides. Computer evidence strongly supports Conjecture 2 for pentagons having an axis of symmetry. Author
- Theoretical Mathematics