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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Zulfatra Lamuda
Program Studi Matematika, Universitas Negeri Gorontalo, Indonesia
Mathematics

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Generalization of Viviani’s Theorem Using a Complex Number Approach on Regular Polygons Inscribed in the Unit Circle Zulfatra Lamuda; Asriadi Asriadi
Jurnal Matematika, Statistika dan Komputasi Vol. 22 No. 3 (2026): May 2026
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v22i3.50210

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.  
Co-Authors Asriadi Asriadi