A circle has one edge/side, that is grade-school geometry. There is no reason to engender confusion by trying to make it into a polygon or introducing infinity. Your model of shapes does not seem to account for curved edges.
Consider a stereotypical pizza slice. One might plainly say that it is a “like a triangle but one edge is curved” without falling into a philosophical abyss. :)
It’s quite useful, though, to understand a curve or arc as having infinite edges in order to calculate its area. The area of a triangle is easy to calculate. Splitting the arc into two triangles by adding a point in the middle of the arc makes it easy to calculate the area… And so on, splitting the arc into an infinite number of triangles with an infinite number of points along the arc makes the area calculable to an arbitrary precision.
A circle has one edge/side, that is grade-school geometry. There is no reason to engender confusion by trying to make it into a polygon or introducing infinity. Your model of shapes does not seem to account for curved edges.
Consider a stereotypical pizza slice. One might plainly say that it is a “like a triangle but one edge is curved” without falling into a philosophical abyss. :)
It’s quite useful, though, to understand a curve or arc as having infinite edges in order to calculate its area. The area of a triangle is easy to calculate. Splitting the arc into two triangles by adding a point in the middle of the arc makes it easy to calculate the area… And so on, splitting the arc into an infinite number of triangles with an infinite number of points along the arc makes the area calculable to an arbitrary precision.