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Have a nice day.

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- Thread starter mech-eng
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- #1

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Have a nice day.

- #2

olivermsun

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As to why the circumference of a circle C = 2*pi*r … I think this is just one of those cases where "the world just works that way." I mean, pi is just defined as the constant such that pi = C / (2r).

- #3

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As to why the circumference of a circle C = 2*pi*r … I think this is just one of those cases where "the world just works that way." I mean, pi is just defined as the constant such that pi = C / (2r).

I know this but without observation how can we understand it should go as far as it is circumference after one revolution. Is there any mathematical idea for this? In other words, why should the way it goes equal to it is circumference and I want to learn that whether this is a stupid question or not? Sometimes we can not see or understand our mistakes.

- #4

Drakkith

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- #5

olivermsun

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Mathematically you could map each point on the wheel to a unique point on the ground, and it would turn out to span 2*pi*r. Or you could imagine wrapping a string around the wheel and then unwinding it on the ground, and it would span 2*pi*r. There are lots of ways to imagine the problem.

- #6

A.T.

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That may take some of the mystery out of it.

- #8

ehild

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You can prove it experimentally with a paper roll as shown in the figure. Draw a mark on the cross section of the cylinder at the end of the sheet. Put the cylinder on the table so the mark points vertically down, and keep the end of the sheet fixed while rolling the cylinder on the table, untill the mark is vertically down again. A certain length of paper is unwound and that length of the piece is equal to the displacement of the centre of the cylinder. Wrap the piece of unwound sheet to the cylinder again: the end will coincide with the mark, so its length is equal to the circumference of the cylinder.

ehild

ehild

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