The purpose of this paper is to establish a conjecture of B. Griinbaum, which states that in every n-polygon P in the plane, n > 5, some diagonals intersect in a pattern that defines a new n-polygon 6 (P), such that the product of the cross-ratios on the diagonals of P is equal to the product of the
✦ LIBER ✦
Polygons, Diagonals, and the Bronze Mean
✍ Scribed by Antonia Redondo Buitrago
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2007
- Tongue
- English
- Weight
- 419 KB
- Volume
- 9
- Category
- Article
- ISSN
- 1590-5896
No coin nor oath required. For personal study only.
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The eigenvalue problem is considered for the Laplacian on regular polygons, with either Dirichlet or Neumann boundary conditions, which will be related to the unit circle by a conformal mapping. The polygonal problem is then equivalent to a weighted eigenvalue problem on the circle with the same bou