The Coexistence of Rotocenters
A bicycle wheel appears to have rotational symmetry: When it is rotated through some angles smaller than 360°, it appears to be in the identical position to the one initially occupied, for the wheel is made up of a number of segments which are mutually congruent to each other. Actually, in practice there is a single valve, used to inflate the tire, which will mark a unique position on the wheel. Conceptually we may ignore the valve, and then determine the smallest angle through which the wheel must turn before it appears to assume its original position. If that angle, expressed in radians, is found to equal θ, then it will appear to assume that position 2π/θ times during a complete rotation. The wheel will then be found to have (2π/θ)-fold rotational symmetry; at the center of the hub there will be a (2π/θ)-fold rotocenter.
KeywordsRotational Symmetry Equilateral Triangle Close Approach Identical Position Unique Position
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