Exact Doubling of Circles, Squares, and Regular Triangles Using Only Straightedge and Compass in Euclidean Geometry
Year: 2026
Type: article
Abstract: This research focuses on finding an exact solution to the problems of “doubling a circle”, "doubling a square" and “doubling a regular triangle”, using only a straightedge and a compass in Euclidean geometry. In 2025, the ancient Greek problem known as "Doubling a Cube" was solved exactly, as documented in https://doi.org/10.14445/22315373/IJMTT-V69I8P506 and https://doi.org/10.36347/sjpms.2025.v12i02.001, [3]. The current problem can be viewed as a derivative issue stemming from the aforementioned Greek challenge. This research aims to determine a circle that possesses double the area of a given circle with area πr², a square that possesses double the area of a given square with area a², and a regular triangle that possesses double the area of a given regular triangle with area A, utilizing only a straightedge and compass within the framework of Euclidean geometry. This research article uses a distinct approach in Geometric Construction to solving the problems.
Author: Tran Dinh Son
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7225634744