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Aristotle, Minor Works, Mechanical Problems (Harvard University Press, Cambridge, MA, 2000), translation by W. S. Hett. Question 15 asks: "Why are the stones on the seashore which are called pebbles round, when they are originally made from long stones and shells? Surely it is because in movement what is further from the middle moves more rapidly. For the middle is the center, and the distance from this is the radius. And from an equal movement the greater radius describes a greater circle. But that which travels a greater distance in an equal time describes a greater circle. Things traveling with a greater velocity over a greater distance strike harder, and things which strike harder are themselves struck harder. So that the parts further from the middle must always get worn down. As this happens to them they become round. In the case of pebbles, owing to the movement of the sea and the fact that they are moving with the sea, they are perpetually in motion and are liable to friction as they roll. But this must occur most of all at their extremities."
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The convex hull is the boundary of the smallest convex region that contains the entire pebble, and can be visualized by imagining a rubber band stretched tight around the pebble.
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The convex hull is the boundary of the smallest convex region that contains the entire pebble, and can be visualized by imagining a rubber band stretched tight around the pebble.
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