Exact Squaring the Circle with Straightedge and Compass by Secondary Geometry

Tran Dinh Son

doi:https://doi.org/10.14445/22315373/IJMTT-V69I6P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 6 | Year 2023 | Article Id. IJMTT-V69I6P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I6P506

Exact Squaring the Circle with Straightedge and Compass by Secondary Geometry

Tran Dinh Son

Received	Revised	Accepted	Published
16 Apr 2023	24 May 2023	07 Jun 2023	17 Jun 2023

Citation :

Tran Dinh Son, "Exact Squaring the Circle with Straightedge and Compass by Secondary Geometry," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 6, pp. 39-47, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I6P506

Abstract

There are three classical problems remaining from ancient Greek mathematics, which are extremely influential in the development of geometry. They are “Trisecting An Angle”, “Squaring The Circle”, and “Doubling The Cube” problems. I solved the first one – Trisecting An Angle and published its paper in the International Journal Of Mathematics Trends And Technology (Volume 69, May 2023). It is difficult to give an accurate date when the problem of Squaring The Circle first appeared. The present article studies what has become the most famous for these problems, namely the problem of squaring the circle or the quadrature of the circle as it is sometimes called. One of the fascinations of this problem is that it has been of interest throughout the whole of the history of mathematics. From the oldest mathematical documents known up to the mathematics of today, the problem and related problems concerning π have interested professional & non-professional mathematicians for millenniums. The problem of Squaring The Circle is stated: Using only a straightedge and a compass, is it possible to construct a square with an area equal to the area of a given circle? I adopt the technique “ANALYSIS” to solve accurately the “Squaring The Circle” problem with only a straightedge & compass by secondary Geometry. Upstream from this method of exact “squaring the circle”, we can deduce, conversely, to get a new Mathematical challenge "Circling the Square", with a straightedge & a compass. In addition, this research result can be used for further research in the “CUBING THE SPHERE” challenge, with only “a straightedge & a compass” using only secondary Geometry.

Keywords

Squaring the circle, Quadrature of the circle, Make a circle squared, Find a square area same as the circle, Circling the square, Make a square rounded.

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