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→The section of a cylinder as a squared circle: tongue-in-cheek statement at end of joke "This simple solution with basic arithmetic and practical common sense elegantly does away with any need for the exact value of the transcendent number pi.."
Looked at from the side it presents a square configuration. Looked at from the end it presents a circular configuration. The perfect circle formed here by crosscut exists as an exactly squared object and the exact square formed here by the same crosscut (twice) exists as a perfectly circular object. The circle has been squared and the square has been circled. What is perfectly round is also exactly square and what is exactly square is also perfectly round. The perfectly round exact square and the exactly square perfect round together are both in essence one object having the same single surface area ''in toto''. This one square and round object has identically the same single volume as itself, in itself, by itself, by the exactly squared shaping of one perfectly round cylinder.
Looked at from the side it presents a square configuration. Looked at from the end it presents a circular configuration. The perfect circle formed here by crosscut exists as an exactly squared object and the exact square formed here by the same crosscut (twice) exists as a perfectly circular object. The circle has been squared and the square has been circled. What is perfectly round is also exactly square and what is exactly square is also perfectly round. The perfectly round exact square and the exactly square perfect round together are both in essence one object having the same single surface area ''in toto''. This one square and round object has identically the same single volume as itself, in itself, by itself, by the exactly squared shaping of one perfectly round cylinder.
If the external surface of the straight side of the cylinder only is opened up and laid flat, its area can be determined by measuring the four sides of the resultant rectangle with a straightedge. The lengths of the top edge and the bottom edge only of the opened and flattened area of the straight sides of the cylinder are identical to the circumference of the circular ends, each length taken and divided by four and rearranged as four equal straight sides of a square, the area of the resultant square determined for one end of the cylinder is then multiplied by two for both ends, and the resulting combined area of the two ends added to the area of the opened and flattened straight side of the cylinder, give the area of the squared-off circular surface of the single cylindrical section with both round ends, the area of this one single squared circle object determined by straightedge measurement (6).
If the external surface of the straight side of the cylinder only is opened up and laid flat, its area can be determined by measuring the four sides of the resultant rectangle with a straightedge. The lengths of the top edge and the bottom edge only of the opened and flattened area of the straight sides of the cylinder are identical to the circumference of the circular ends, each length taken and divided by four and rearranged as four equal straight sides of a square, the area of the resultant square determined for one end of the cylinder is then multiplied by two for both ends, and the resulting combined area of the two ends added to the area of the opened and flattened straight side of the cylinder, give the area of the squared-off circular surface of the single cylindrical section with both round ends, the area of this one single squared circle object determined by straightedge measurement (6).
This simple solution with basic arithmetic and practical [[common sense]] elegantly does away with any need for the exact value of the transcendent number '''<big><big>π</big></big>''' ''pi'' and the [[Cylinder|formula]] '''<math> S= 2\pi r^2 + 2\pi r h \ .</math>''']]
No one takes this seriously as being properly related in any way to an actual solution of the classical problem posed by the ancient geometers, as a real solution to an insoluble problem in six simple steps.
No one takes this seriously as being properly related in any way to an actual solution of the classical problem posed by the ancient geometers, as a real solution to an insoluble problem in six simple steps.