Abstract
Squaring the circle, the construction of a square with the same area as a given circle, is one of the three construction problems that the Greeks posed but were unable to solve. Unlike trisecting the angle and doubling the cube, where the impossibility follows from properties of the roots of polynomials, the impossibility of squaring the circle follows from the transcendentality of 𝜋: it is not the root of any polynomial with rational coefficients. This is a difficult theorem that was proved in 1882 by Carl von Lindemann.
Download chapter PDF
Author information
Authors and Affiliations
Rights and permissions
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Copyright information
© 2022 The Author(s)
About this chapter
Cite this chapter
Ben-Ari, M. (2022). Squaring the Circle. In: Mathematical Surprises. Springer, Cham. https://doi.org/10.1007/978-3-031-13566-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-031-13566-8_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-13565-1
Online ISBN: 978-3-031-13566-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)