Generalization of Viviani’s Theorem Using a Complex Number Approach on Regular Polygons Inscribed in the Unit Circle

Zulfatra Lamuda; Asriadi Asriadi

doi:10.20956/j.v22i3.50210

Authors

Zulfatra Lamuda Program Studi Matematika, Universitas Negeri Gorontalo, Indonesia
Asriadi Asriadi Program Studi Matematika, Universitas Negeri Gorontalo, Indonesia

DOI:

https://doi.org/10.20956/j.v22i3.50210

Keywords:

Viviani’s Theorem, Regular Polygon, Unit Circle, Complex Number

Abstract

One of the classical theorems in geometry is Viviani’s Theorem. This theorem states that for any interior point of an equilateral triangle, the sum of the perpendicular distances from that point to each triangle side equals the triangle’s height. Therefore, this study aims generalize the property contained in Viviani’s Theorem to regular polygons inscribed in the unit circle using a complex number approach. The results of this study show that the obtained constant is n⋅ cos (π/n ), where nϵN. This constant replaces the height of the equilateral triangle as stated in Viviani’s Theorem.

References

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