RE: Is there an infinite range of perfect circles.
May 14, 2022 at 10:31 am
(This post was last modified: May 14, 2022 at 10:40 am by polymath257.)
(May 13, 2022 at 6:48 pm)Thumpalumpacus Wrote:(February 25, 2022 at 1:54 pm)highdimensionman Wrote: Sort of It's a video that I saw on youtube math video about a month and a half ago can't find it now that furthered my thinking, there was something odd about the centre measurement and the shape had 3 curved corners and 3 curved sides i think and it was closeish to circular.
It's a shame I can't find the video now.
"Corners" implies a different length, because corners are declivities in a given space. If you've got corners, your radii aren't equal all the way 'round, which is the definition of a circle.
Take a standard equilateral triangle. From each vertex, draw a circle with radius to the other vertices. You will obtain a 'fat' triangle with circular sides.
That figure is an equidiameter figure: it is the same width in every direction. But it is not a circle. It has 'corners'.
This can be generalized for any regular polygon with an odd number of sides.
