Two Regular Polygons with a Shared Vertex

Mamuka Meskhishvili

doi:10.26713/cma.v13i2.1944

Authors

Mamuka Meskhishvili Department of Mathematics, Georgian-American High School, 18 Chkondideli Str., Tbilisi 0180, Georgia https://orcid.org/0000-0003-2970-6480 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v13i2.1944

Keywords:

Bottema theorem, Cyclic averages, Regular polygon, Common vertex

Abstract

For two non-congruent regular polygons of the same type, the method of finding a point in the plane at the equal distances to the vertices, is established. The existence of two points with this property is proved for two polygons with a shared vertex. For one of them, it is proved that it satisfies the Bottema theorem conditions and based on this, the generalized Bottema theorem for any two regular polygons is given.

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