Let's say that someone is drawing a circle with a compass. As that circle is being drawn a second compass is attached to the first such that the needle leg is attached to the pencil of the first. Only instead of a needle it is a small wheel. As the first compass inscribes its circle the second compass is tracing out the circumference of the first and drawing a circle at twice the rate of rotation of the first. An analogy would be someone at the edge of a merry-go-round that is rotating above a piece of paper. The rider endeavors to trace out a circle on the paper as the merry-go-round rotates at twice the rate of rotation of the merry-go-round. Is there an exponential relation between the relative rates of rotation and the area incribed under the curve created by the second compass? Additionally, if a third compass rode on the path inscribed by the second attempting to sketch a circle at some ratio of the rate of rotation of the first and second could that area be expressed? (Please private message as well as post.)(adsbygoogle = window.adsbygoogle || []).push({});

Thank you,

Duhoc

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# Tough Question in Calculus

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