Is there an infinite range of perfect circles.

[Jehanne]

[GrandizerII]

And we similarly define a sphere in three dimensions the same way. The same definition even works in any metric space, although there are some counter-intuitive situations in that generality.

There is a another curved shape that follows as a set of all points that are equidistant from a given point. Unfortunately I can't remember what the geometry was called and can't find it anywhere now. I'll keep looking though.

Do you mean another shape in 2d realm besides the circle? I fail to see what that could be.

[polymath257]

There is a another curved shape that follows as a set of all points that are equidistant from a given point. Unfortunately I can't remember what the geometry was called and can't find it anywhere now. I'll keep looking though.

Do you mean another shape in 2d realm besides the circle? I fail to see what that could be.

He may be confused about equi-diameter figures. These do not have to be circles.

[Fireball]

Eh, he strikes me as uneducated in geometry and algebra. Maybe he's channeling parabolas, and left out the directrix?

[highdimensionman]

Do you mean another shape in 2d realm besides the circle? I fail to see what that could be.

He may be confused about equi-diameter figures. These do not have to be circles.

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.

[highdimensionman]

I was thinking about other shapes and solids of constant width but the video I had watched had confused me a little.

[Thumpalumpacus]

He may be confused about equi-diameter figures. These do not have to be circles.

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.

[polymath257]

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.

[UniversesBoss]

Yes and they are getting tighter.