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.
Instead of “has infinite digits”, I prefer to say that it CANNOT be expressed as a base10/decimal number. If you choose a different base (base-pi for example), then it very much has finite digits… :)
It can’t be expressed in any integer-based notation without an infinite number of digits. Only when expressed in some bases which are themselves, irrational. It’s infinity either way.
Or zero…
Probably More accurate to say it has an infinite number of edges
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.
Or you could just enjoy your π
The number which famously has an infinite number of digits? I thought we were arguing against the real-ness of infinity.
Also note: the method I was describing is one of the ways in which pi can be calculated.
Instead of “has infinite digits”, I prefer to say that it CANNOT be expressed as a base10/decimal number. If you choose a different base (base-pi for example), then it very much has finite digits… :)
It can’t be expressed in any integer-based notation without an infinite number of digits. Only when expressed in some bases which are themselves, irrational. It’s infinity either way.
therefore ∞ = 0 😀👍