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Generalization of Viviani’s Theorem Using a Complex Number Approach on Regular Polygons Inscribed in the Unit Circle
Jurnal Matematika, Statistika dan Komputasi
ISSN 2614-8811, 1858-1382
Published 2026-05-14
Publisher Department of Mathematics, Hasanuddin University
Language en
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.
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Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai,
first harvested 5 Nov 2026,
last seen 5 Nov 2026.
Original metadata (oai_dc)
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<dc:title xml:lang="en">Generalization of Viviani’s Theorem Using a Complex Number Approach on Regular Polygons Inscribed in the Unit Circle</dc:title>
<dc:creator xml:lang="en">Lamuda, Zulfatra</dc:creator>
<dc:creator xml:lang="en">Asriadi, Asriadi</dc:creator>
<dc:subject xml:lang="en">Viviani’s Theorem</dc:subject>
<dc:subject xml:lang="en"> Regular Polygon</dc:subject>
<dc:subject xml:lang="en">Unit Circle</dc:subject>
<dc:subject xml:lang="en">Complex Number</dc:subject>
<dc:description xml:lang="en">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.
</dc:description>
<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
<dc:date>2026-05-14</dc:date>
<dc:type>info:eu-repo/semantics/article</dc:type>
<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
<dc:format>application/pdf</dc:format>
<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/50210</dc:identifier>
<dc:identifier>10.20956/j.v22i3.50210</dc:identifier>
<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 22 No. 3 (2026): May 2026; 743-760</dc:source>
<dc:source>2614-8811</dc:source>
<dc:source>1858-1382</dc:source>
<dc:language>en</dc:language>
<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/50210/14424</dc:relation>
<dc:rights xml:lang="en">Copyright (c) 2026 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>
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APA 7
Lamuda, Z., & Asriadi, A. (2026). Generalization of Viviani’s Theorem Using a Complex Number Approach on Regular Polygons Inscribed in the Unit Circle. Jurnal Matematika, Statistika dan Komputasi, 22(3), 743–760. https://doi.org/10.20956/j.v22i3.50210
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IEEE
Z. Lamuda and A. Asriadi, “Generalization of Viviani’s Theorem Using a Complex Number Approach on Regular Polygons Inscribed in the Unit Circle,” Jurnal Matematika, Statistika dan Komputasi, vol. 22, no. 3, pp. 743–760, 2026, doi: 10.20956/j.v22i3.50210.
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