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Unformatted text preview: for discovering formulas which then had to be verified by an accepted method of proof. The approach uses an identity to show that the shaded disks just balance. The circle x 2 + y 2 = 2 ax gives rise to the identity, ! x 2 + y 2 = 2 ax . This gives rise to 2 a ( x 2 + y 2 ) = x (2 a ) 2 showing that the disks just balance assuming that the connecting arms are massless and that the fulcrum is at the left face of the cylinder. Since the masses and center of masses are known for the cylinder and the cone, the only unknown mass is that of the sphere. For the figures to balance sphere must have volume V = 4 3 a 3 . 2 a 2 a y 2 a 2 a 2 a x x x 2 y 2 2 a...
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- Spring '07