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→The section of a cylinder as a squared circle: alternate joke solution to squaring the circle by opening up and flattening the cylinder's vertical side, folding it twice, then joining the 2 side edges of the 4 flat sections to make the end a square
This simple solution using basic arithmetic and practical [[common sense]] in six simple steps 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>'''
This simple solution using basic arithmetic and practical [[common sense]] in six simple steps 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>'''
Alternatively, the length of the top or bottom edge of the (hollow) flattened vertical cylinder is identical to the circumference of the circular end of the round cylinder (1), and the flattened rectangle of the side of the formerly round cylinder can be folded in half side to side, presenting two joined halves with a vertical center crease (2), and then the two joined halves together are folded again, center crease to side edges resulting in three creases, four vertical sections and two side edges (3), then opening up the folded flattened and creased vertical side of the formerly round cylinder while retaining the three resultant vertical creases, the two side edges can be joined, producing a vertical rectangular prism equal in length to the original cylinder, with four equal vertical sides, each of the four sides in horizontal width equal to one-fourth the width of the rectangle, which is identical to the flattened horizontal circumference of the formerly round cylinder joined at the two vertical edges (4), the three vertical creases each stabilized with the four vertical sides, each side set at right angles to its two adjoining sides (four sides at 90<sup>o</sup> horizontal angles), the upper horizontal edge of the four sections of the vertical side of the flattened cylinder joined at the two side edges forming a square end (5), the two resulting top and bottom square ends of the prism formed from the opened and flattened former cylinder folded and creased now each enclose with their four outer edges as a square end the same area as the circular end of the cylinder from which the flattened rectangular form was obtained. The area bounded by the outer edge of the circular configuration at the end of the cylinder is equal to the area bounded by the length of its circumference, straightened out, folded twice, creased, opened up, joined at the side edges with its folds at 90<sup>o</sup>, resulting in a square configuration. The circle has been squared, and the area of the square so formed from the circumference of the circle equals the area of the circle from which the square was derived.