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Theorems on regular polygons
- A property of the regular heptagon
- Some properties of a regular heptagon
- Some properties of a regular nonagon
- A property of the regular nonagon
- Some interesting properties of the regular decagon
- Regular pentagon erected internally on a side of a regular decagon
- Touching pentagons
- Some properties of a regular 11-gon
- Some properties of a regular 13-gon
- Some properties of a regular 17-gon
- Unit lengths in the regular 19-gon
- A theorem on regular n-gons (n is even)
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Theorems on regular polygons
Zoltán Kovács, Feb 27, 2018
Watkins and Zeitlin (1993) published a method to simply compute the minimal polynomial of cos(2π/n), based on the Chebyshev polynomials of the first kind. By using their method GeoGebra is able to prove various properties of regular n-gons since November 2017. This collection demonstrates how useful this new feature is. As a further improvement of the Watkins-Zeitlin method, another software tool RegularNGons can be used to automatically find interesting features of a regular polygon.
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1. A property of the regular heptagon
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2. Some properties of a regular heptagon
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3. Some properties of a regular nonagon
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4. A property of the regular nonagon
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5. Some interesting properties of the regular decagon
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6. Regular pentagon erected internally on a side of a regular decagon
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7. Touching pentagons
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8. Some properties of a regular 11-gon
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9. Some properties of a regular 13-gon
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10. Some properties of a regular 17-gon
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11. Unit lengths in the regular 19-gon
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12. A theorem on regular n-gons (n is even)
A property of the regular heptagon
Consider the construction above. It is a regular 7-gon with some diagonals, their intersection points and a segment joining them. Remark that HI=2AB, moreover A is the midpoint of HI.
This theorem has been obtained automatically by using the software tool RegularNGons.
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