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Journal for Geometry and Graphics 09 (2005), No. 2, 119--132
Copyright Heldermann Verlag 2005

Geometry of Regular Heptagons

Zvonko Cerin
Dept. of Mathematics, University of Zagreb, Kopernikova 7, 10010 Zagreb, Croatia

This paper explores some new geometric properties of regular heptagons. We add to the list of results from the Bankoff-Garfunkel famous paper on regular heptagons 30 years ago enlisting the help from computers. Our idea is to look at the central points (like incenters, centroids, circumcenters and orthocenters) of certain triangles in the regular heptagon to find new related regular heptagons which have simple constructions with ruler and compass from the original heptagon. In the proofs we use complex numbers and the software Maple V. The eleven figures are made with the Geometer's Sketchpad.

Keywords: Regular heptagon, heptagonal triangle.

MSC: 51N20; 51M04, 14A25, 14Q05

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