Pure and Applied Mathematics Quarterly
Volume 16 (2020)
Special Issue: In Honor of Prof. Kyoji Saito’s 75th Birthday
Guest Editors: Stanislaw Janeczko, Si Li, Jie Xiao, Stephen S.T. Yau, and Huaiqing Zuo
On the area formulas of inscribed polygons in classical geometry
Pages: 557 – 572
We show that there is no area formula of the general inscribed $n$‑gon for $n \geq 5$ only by using arithmetic operations and $k$‑th roots of its side lengths in classical geometry.
Euclidean geometry, hyperbolic geometry, spherical geometry
2010 Mathematics Subject Classification
Primary 51Kxx. Secondary 51M10, 51N20.
Received 20 June 2019
Accepted 13 August 2019
Published 11 November 2020