Automated Detection of Interesting Properties in Regular Polygons
Keyword(s):
Abstract We demonstrate a systematic, automated way of discovery of a large number of new geometry theorems on regular polygons. The applied theory includes a formula by Watkins and Zeitlin on minimal polynomials of $$\cos \frac{2\pi }{n}$$ cos 2 π n , and a method by Recio and Vélez to discover a property in a plane geometry construction. This method exploits Wu’s idea on algebraizing the geometric setup and utilizes the theory of Gröbner bases. Also a bijective function is given that maps the investigated cases to the first natural numbers. Finally, several examples are shown that are all previously unknown results in planar Euclidean geometry.
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2018 ◽
2010 ◽
Vol 153
(2)
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pp. 363-396
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2009 ◽
Vol 23
(2)
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pp. 571-595
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2001 ◽
Vol 338
(1-3)
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pp. 171-199
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