Abstract—The paper outlines a new approach to solving the classical Greek problem ‘squaring the circle’ in a constructive manner with a major focus on its application in practice. Though it is known that the problem of squaring the circle cannot be solved by means of Euclidean construction, this paper will provide an insight into innovative solutions to the problem using only a ruler and compass. The solution for squaring the circle is based on finding the original ratio of 11,000,000: 3,005,681. Squaring the circle leads to the introduction of a parameter and derived functional links which indicate the possibility of applying problems in practice by determining and calculating areas of related geometric figures on a flat plane and by calculating the volumes of related geometrical figures in space through specific examples such as turning the Pyramid of Cheops into the cone of the same volume, or a Leaning Tower of Pisa into the shape of a prism.

Keywords—Application, construction, geometry, squaring the circle

Cite: Veselin Rmuš, "Application of Squaring the Circle in Practice," International Journal of Applied Physics and Mathematics, vol. 14, no. 1, pp. 1-11, 2024.

Copyright © 2024 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).