This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using only an unmarked ruler and a compass), produced a square equal in area to the given circle, which is 50 cm2. This result was a clear demonstration that not only is the construction valid for the squaring of a circle of any radius, but it is also capable of achieving absolute results (independent of the number pi (π), in a finite number of steps), when carried out with precision.
References
[1]
Tietze, H. (1965) Famous Problems in Mathematics. Graylock Press, New York.
[2]
Barton, L.O. (2022) A Procedure for Trisecting an Acute Angle. Advances in Pure Mathematics, 12, 63-69. https://doi.org/10.4236/apm.2022.122005
[3]
O’Connor, J.J. and Robertson, E.F. (1999) Squaring the Circle. https://mathshistory.st-andrews.ac.uk/HistTopics/Squaring_the_circle/
[4]
Barton, L.O. (2022) A Method for the Squaring of a Circle. Advances in Pure Mathematics, 12, 535-540. https://doi.org/10.4236/apm.2022.129041
[5]
Barton, L.O. (1993) Mechanism Analysis, Simplified Graphical and Analytical Techniques. 2nd Edition, Marcel Dekker, New York.
[6]
Wilson, C.E. and Sadler, J.P. (1993) Kinematics and Dynamics of Machinery. 2nd Edition, Harper Collins College Publishers, New York.
[7]
Barton, L.O. (1991) Applying the Mean Proportional Principle to Graohical Solutions. Engineering Design Graphics Journal, 5, 34-41.
[8]
Barton, L.O. (1992) A Graphical Method for Solving the Euler-Savary Equation. Journal of Engineering Technology, 9, 27-32.
[9]
Bennet, D. (2002) Exploring Geometry with Geometer’s Sketch Pad. Key Curriculum Press, Emeryville, GA.