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

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

JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Vol. 22 No. 3 (2026): May 2026

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.