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HSCI 3013 
History of Science to the Age of Newton

Discussion Exercise 6

Tusi couples


1. Figure A shows the simplest pattern of a Tusi couple: a pair of circles, one half the size of the other. As the large circle rotates to the left (anticlockwise) the small circle rotates to the right (clockwise) at twice the speed. The large circle will carry the small circle into a succession of new positions as it rotates (figures A2 -- A5). To visualize the result, imagine both circles as clock faces. The two reference points, > on the large circle and >> on the small circle, both start at 12 o'clock (figure A1).


1.1) Draw in the position of the >> marker on the inner circle in A2 -- A5. Remember that the small circle rotates twice as fast as the large one.

1.2) The important question: What overall pattern does the >> marker trace out as the two circles move? Is this embarrassing to Aristotle?


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