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→The section of a cylinder as a squared circle: at beginnin of mathematical joke added the tease " Using only a straightedge ruler and a compass, a solution is obtained in six simple steps."
===The section of a cylinder as a squared circle===
===The section of a cylinder as a squared circle===
As a mathematical joke, a circle can simultaneously present a square if a perfectly round, solid [[cylinder]] is produced with a sectional length equal to its measured diameter.
As a mathematical joke, a circle can simultaneously present a square if a perfectly round, solid [[cylinder]] is produced with a sectional length equal to its measured diameter. Using only a straightedge ruler and a compass, a solution is obtained in six simple steps.
The straightedge determines the exactitude of the first straight smooth cut across the round cylinder at a right angle to the straight body of the cylinder (1). The compass point is placed at what is determined to be the exact center of the diameter of the round crosscut end of the solid cylinder, and the stylus is adjusted to the outer edge of the cut and rotated around the edge to determine with exactitude the center of the crosscut and the length of the radius of the cut (2). The span of the compass is then fixed and it is then moved 90<sup>o</sup> to the straight side of the cylinder and positioned with the stylus at the exact edge of the crosscut, with the point of the compass positioned exactly at a 90<sup>o</sup> angle from the edge of the cut (3). The stylus of the compass is then rotated 180<sup>o</sup> away from the edge of the first crosscut end to determine with exactitude where to make the second right angle cut across the cylinder (4). The second straightedge smooth crosscut of the cylinder makes a finished cylinder section with a measured exact length identical to the measured exact diameter of the cylinder, a cylindrical section exactly as long as it is wide (5).
The straightedge determines the exactitude of the first straight smooth cut across the round cylinder at a right angle to the straight body of the cylinder (1). The compass point is placed at what is determined to be the exact center of the diameter of the round crosscut end of the solid cylinder, and the stylus is adjusted to the outer edge of the cut and rotated around the edge to determine with exactitude the center of the crosscut and the length of the radius of the cut (2). The span of the compass is then fixed and it is then moved 90<sup>o</sup> to the straight side of the cylinder and positioned with the stylus at the exact edge of the crosscut, with the point of the compass positioned exactly at a 90<sup>o</sup> angle from the edge of the cut (3). The stylus of the compass is then rotated 180<sup>o</sup> away from the edge of the first crosscut end to determine with exactitude where to make the second right angle cut across the cylinder (4). The second straightedge smooth crosscut of the cylinder makes a finished cylinder section with a measured exact length identical to the measured exact diameter of the cylinder, a cylindrical section exactly as long as it is wide (5).