Has circle $0$ edges or infinite edges?

Question

Today I studied about circle that it is a closed figure with $0$ edges.

Then I thought about a wire with fixed length and tried to make closed polygons of edges $3,4,5\ldots$

I saw that the figure looks more closer to circle when edges are increased

So can I conclude that circle is a closed polygon of infinite edges and not of $0$ edges??

I am really confused.

Answer 1

I always thought a circle had 2 sides - an in-side and an out-side :-)

More seriously, infinite limits are tricky things, since the set of points which define a circle are infinitely close together, there is no edge between them, so from that perspective a circle has 0 sides.

That said, we can define projections which convert (infinitlely long) straight lines to circles: https://en.m.wikipedia.org/wiki/Stereographic_projection So from that perspective you could say it has 1 side.

This is all by way of saying that it very much depends on how you define an edge.

Answer 2

A side is defined to be a line segment between $2$ points. In a circle, the points are infinitely close together, making impossible to fit a line between them. Therefore a circle, geometrically, would have $0$ sides.

If a circle were to be allowed to have any amount of sides, then theoretically any side can be split up into multiple sides with a $180^\circ$ angle, creating a situation where a square has $56$ sides.

Answer 3

If an edge of a closed figure has to be straight, then a circle has no edges, since no part of a circle's circumference is straight. If edge is defined so as to apply to more than just rectilinear figures, e.g. as any portion of a closed figure between two vertices, i.e. between two points not characterized by unique tangents, then the portion of a pointed arch between its apex and base, is also an edge. But again, a circle, or an ellipse, would have no edges, since tangents to any two points on either of these figures are unique: the figures have no vertices. Counting its base, the pointed arch would have three edges I guess, since there's no unique tangent to apex or to the ends of the base. But yes (@Henry), "edge" has to be defined. And I have to be careful about "vertex" too, since the vertex of an ellipse, i.e. the end of its major axis, does have a unique tangent.