This book offers a comprehensive and historically grounded exploration of the geometric and algebraic construction of regular polygons. Starting with problems rooted in antiquity—such as the construction of the triangle, square, and pentagon—it moves through medieval Islamic advances in heptagon construction and culminates in the revolutionary 1796 work of Carl Friedrich Gauss, who proved that a regular 17-gon can be constructed with just a ruler and compass. The author methodically traces the development of this mathematical challenge, linking geometric constructions to algebraic solutions, especially through the cyclotomic equation xn−1=0x^n – 1 = 0, and highlighting the critical roles of Descartes, Lagrange, and Gauss.
Structured in nine chapters, the book blends history, rigorous mathematics, and a pedagogical approach suitable for advanced secondary school students. It presents more than 50 different constructions of the regular pentagon and over 15 for the heptadecagon, many of which are rarely seen or completely absent in standard texts. Algebraic and geometric methods are carefully explained and complemented by detailed constructions and proofs. Special emphasis is placed on maintaining clarity and accessibility without sacrificing mathematical depth, making it a unique and invaluable resource on a subject often treated fragmentarily in modern literature.
Authors
- Djura Paunić
Subjects
- Geometry
Book Details
- Hardcover: 356 pages
- Publisher: XYZ Press (2025)
- Language: English
- ISBN-13: 979-8-9917692-4-2
