That’s exactly my point, there are two different colloquial ways of talking about angles. I am not claiming there is a mathematical inconsistency.
Colloquially, a “triangle has 180 degrees” and a “circle has 360 degrees.” Maybe that’s different in different education systems, but certainly in the US that’s how things are taught at the introductory level.
The sum of internal angles for a regular polygon with n sides is (n-2)×pi. In the limit of n going to infinity, a regular polygon is a circle. From above it’s clear that the sum of the internal angles also goes to infinity (wheres for n=3 it’s pi radians, as expected for a triangle).
There is no mystery here, I am just complaining about sloppy colloquial language that, in my opinion, doesn’t foster good geometric intuition, especially as one is learning geometry.
That’s exactly my point, there are two different colloquial ways of talking about angles. I am not claiming there is a mathematical inconsistency.
Colloquially, a “triangle has 180 degrees” and a “circle has 360 degrees.” Maybe that’s different in different education systems, but certainly in the US that’s how things are taught at the introductory level.
The sum of internal angles for a regular polygon with
nsides is(n-2)×pi. In the limit of n going to infinity, a regular polygon is a circle. From above it’s clear that the sum of the internal angles also goes to infinity (wheres for n=3 it’s pi radians, as expected for a triangle).There is no mystery here, I am just complaining about sloppy colloquial language that, in my opinion, doesn’t foster good geometric intuition, especially as one is learning geometry.