Chris Park wrote:Interesting, I never thought to generalize a definition for 2d shapes other than circles in support of which constant is more natural.
Chris Park wrote:Can you explain your first step, though? Where is the origin in your coordinate system containing ? For instance, if is a circle and the origin is at its (bary)center, wouldn't
Or can the origin be anywhere in ? Forgive me if I've got it wrong, I'm more of an engineering/physics guy and not used to set notation.
Chris Park wrote:The triangle appears to be the 'worst case scenario' in terms of drawing a shape with diameter D whose exceeds as much as possible without changing D. Even in this shape, however, the perimeter is still only .
Nyarly wrote:The perimeter of the Reuleaux triangle (and every Reuleaux polygon) is , in fact it is made of three circular arc of radius and subtended angle . Then
Chris Park wrote:Interesting that we've just brought up the similarity of all Reuleaux n-gons in having perimeters . When you start looking at this subset of polygons, radius becomes a player again (since it's easy to define the radius of a Reuleaux n-gon).
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