I was talking to a friend about stretching something end a circular drum's "edges". We offered google a shot and it seems like civilization are unsure if there room one, zero, or boundless edges. On a semantic level, is the ok to say I stretched it about the "edges" or should it it is in "edge"?

I would certainly say it's similar to questioning "Does the US have two borders (one with Canada, one v Mexico) or deserve to you talk around 'the border' the the joined states?"

Polygons room categorized by the variety of edges your edge is separated into. A circle plainly has "an edge", in order to ask "how many" you have to think of a circle together a polygon, which that is not.

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So a circle, prefer every limited shape, has actually an edge. Even the greeks favored to think of a circle together a degenerate polygon, and also for polygon we usually talk about "edges" rather of "the edge," however technically a circle is not a polygon for this reason technically that doesn't make sense to questioning how numerous edges.

That's simply one perspective, the word edge is identified in various ways in different places. Together a CW complex a circle might have 2 edges. As a topological an are it might have no sheet if girlfriend embed that correctly.

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· 8y

A drum is, because that a better term, a cylinder. You space stretching the skin over and past the peak edge the the cylinder.

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Op · 8y

Thanks because that answering mine question. I'm starting to recall every one of the things I have actually forgotten native geometry class.

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· 8y

What's your meaning of leaf when applied to a circle? relying on your definition you could have 0, 1, or boundless edges, even when the same definition gives you the ideal answer because that polygons.

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· 8y

It counts on just how you define an "edge".

If you take into consideration an leaf to it is in a subset of points intersecting with some tangent line, then a circle has actually an infinite variety of edges (one because that each point, due to the fact that every tangent line intersects at exactly one point).

But friend could also define the to be a non-degenerate subset of points intersecting a tangent line. Non-degenerate right here would median "contains at least two points". A circle would have zero edge under this definition.

For polygons, this two meanings coincide. Under either, a square has 4 edges, and also an n-gon has n.

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You could probably also create a suitable an interpretation that to be the exact same for polygons, however for a circle, offers you simply one edge. My guess is the you would want to define it in regards to "connected subsets of continuous curvature" or miscellaneous similar. The circle would certainly obviously fulfill such a definition, and for polygons, it would certainly hinge on the fact the curvature isn't well-defined other than for on subsets we would certainly intuitively think about the edges.