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The drawing method of turning a circle into a square explored in this study does not need the circumference of a circle, nor does it need to draw a line segment equal to a circle or an arc. It only needs to draw 1800 arcs and diameters and draw a right triangle on a semicircle with the hypotenuse R as a right-angled side, and the square of the other right-angled side reaches 95.49% of the area of the circle. According to the Pythagorean theorem, the square of the other right-angled side can be increased. When the trial coefficient K = 0.9265, The square of the other right-angled side is equal to the area of the circle by 5 digits. In the process of continuing to try, a formula for calculating k is found, so that the diameter of the given circle is a right-angled triangle with the hypotenuse K*R as the right-angled side, and the square of the other right-angled side is equal to s =√(πR2 ) .
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Using the Pythagorean Theorem to Make a Square Equal to the Area of a Circle
How to cite this paper: Jiucheng Zhong. (2024) Using the Pythagorean Theorem to Make a Square Equal to the Area of a Circle. Journal of Applied Mathematics and Computation, 8(4), 308-312.
DOI: http://dx.doi.org/10.26855/jamc.2024.12.004