DOI: https://doi.org/10.36347/sjpms.2024.v11i10.004

Pages: 150-159

No great theory lasts forever in science, but only specific research and discoveries continuously complement each other. There have been 3 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. 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 a given circle? From the oldest mathematical documents known up to today's mathematics, the "Squaring the Circle" problem and related problems concerning π have interested professional & non-professional mathematicians for millenniums. I adopted the technique “ANALYSIS” to solve accurately the “Squaring the Circle” problem with only a straightedge & compass by Euclidean Geometry, and did not use the value π/Pi anywhere in this exact solution. Upstream from this method of exact “squaring the circle”, we can deduce, inversely, to get a new Mathematical challenge "Circling the Square" with a straightedge & a compass.