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# Rolling a circle within a circle

13 replies to this topic

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Posted 09 July 2013 - 12:44 PM

Spoiler for

Modifed though, as the circle is within your circle. Also if it rotates from 12 to 3, 3 to 6, 6 to 9 and comes back to start, that is four rotations, right?
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### #12 k-man

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Posted 09 July 2013 - 03:35 PM

The small circle makes a full revolution when the point p is in the same orientation as before, not when point p touches the large circle again.

Spoiler for a picture is worth a thousand words

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### #13 bonanova

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Posted 10 July 2013 - 06:45 AM

Spoiler for

Modifed though, as the circle is within your circle. Also if it rotates from 12 to 3, 3 to 6, 6 to 9 and comes back to start, that is four rotations, right?

Yes, modified; yet similar.

Both require the consideration that traversing a circular path (inside or out)

affects the coin/circle in the same way that a rotation does, as it traverses that path.

No, not four rotations - see k-man's picture.

A rotation occurs each time the point p returns to its initial azimuth.

Not each time the point p touches the outer circle.

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Posted 10 July 2013 - 06:21 PM

Spoiler for

Modifed though, as the circle is within your circle. Also if it rotates from 12 to 3, 3 to 6, 6 to 9 and comes back to start, that is four rotations, right?

Yes, modified; yet similar.

Both require the consideration that traversing a circular path (inside or out)

affects the coin/circle in the same way that a rotation does, as it traverses that path.

No, not four rotations - see k-man's picture.

A rotation occurs each time the point p returns to its initial azimuth.

Not each time the point p touches the outer circle.

nicely done! I forgot to consider, in my own calculation, that the point p touches the circle more often than it does coming back to its starting position.  which makes sense since it goes to the line before it comes back to its starting position on every spin.

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