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"The circle is the only figure which has the same width in all directions."

Can someone explain? What exactly do they mean by width and what else has this property?

If you think of the figure as lying in the x-y plane, then its projection onto one of the axes has the same length no matter the orientation of the figure. One nifty example of this is the Reuleaux triangle, which is related to the mechanics of rotary engines.

http://en.wikipedia.org/wiki/Reuleaux_triangle

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