The lady also could have noted that, while the point on the rim of a circle that rolls one full turn defines a cycloid, the point at the circle's center defines a line segment. The cycloid and the line segment represent the maximum and minimum distances traveled by any points on the rolling circle. Any point between the circle's rim and its center, depending on its distance from each, will describe a wavy line segment whose shape and length will vary between a full-on cycloid and a straight line segment. The lady does illustrate this with the clever use of a physical model, but she doesn't really explain what's going on, geometrically speaking.
Thursday, June 18, 2020
Aristotle's paradox of the wheel
Interesting bit of math and philosophy, although the lady takes way too long to express the Euclidean idea that there are infinite points between any two points on a line.
The lady also could have noted that, while the point on the rim of a circle that rolls one full turn defines a cycloid, the point at the circle's center defines a line segment. The cycloid and the line segment represent the maximum and minimum distances traveled by any points on the rolling circle. Any point between the circle's rim and its center, depending on its distance from each, will describe a wavy line segment whose shape and length will vary between a full-on cycloid and a straight line segment. The lady does illustrate this with the clever use of a physical model, but she doesn't really explain what's going on, geometrically speaking.
The lady also could have noted that, while the point on the rim of a circle that rolls one full turn defines a cycloid, the point at the circle's center defines a line segment. The cycloid and the line segment represent the maximum and minimum distances traveled by any points on the rolling circle. Any point between the circle's rim and its center, depending on its distance from each, will describe a wavy line segment whose shape and length will vary between a full-on cycloid and a straight line segment. The lady does illustrate this with the clever use of a physical model, but she doesn't really explain what's going on, geometrically speaking.
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