Doesn't a circle imply that there's the same radius all the way around?

My perfect circles are probably casino chips. I suppose their infinite range could be denominations.

(February 22, 2022 at 8:48 pm)arewethereyet Wrote: Doesn't a circle imply that there's the same radius all the way around?

Yes. In geometry, we define a circle as "the set of all points in a plane that are equidistant from a given point, called the center of the circle". The question posed by the OP shows ignorance of this basic concept.

(February 22, 2022 at 7:59 pm)polymath257 Wrote: Sorry, I could not parse your question.

At best, this is confused. At worst, it is nonsense.

The OP reminds me of some scientific papers (such as the Sokal hoax) that were spoofs but managed to get published anyway. This is, of course, how creationists, IDers, and others (WLC) operate, by barfing strands of technobabble to confuse the unwary. When I first read the OP, it seemed legit, some strange area of typology, but as I reread it, I got the impression that he is just trolling.

(February 22, 2022 at 9:27 pm)Fireball Wrote:

(February 22, 2022 at 8:48 pm)arewethereyet Wrote: Doesn't a circle imply that there's the same radius all the way around?

Yes. In geometry, we define a circle as "the set of all points in a plane that are equidistant from a given point, called the center of the circle". The question posed by the OP shows ignorance of this basic concept.

It's pretty damn basic if I get it.

(February 22, 2022 at 9:32 pm)arewethereyet Wrote:

(February 22, 2022 at 9:27 pm)Fireball Wrote: Yes. In geometry, we define a circle as "the set of all points in a plane that are equidistant from a given point, called the center of the circle". The question posed by the OP shows ignorance of this basic concept.

It's pretty damn basic if I get it.  

Yup. You get it. OP? Well...no.

I'm still struggling to understand what the OP is saying exactly, but I don't think they're clueless about the basics of a circle. I think they're expressing some confusion about perfect circles in the metaphysical sense? And how 2d figures evolve into 3d and higher-dimension figures as you go higher and higher in dimensions?

To answer the thread title, yes, there is an infinite range of perfect circles, since each of an infinite number of radius lengths can correspond to its own perfect circle.

ETA: Speaking of perfection in the geometrical sense, I see the circle as the perfect shape among all 2d shapes, sphere as the perfect shape among all 3d shapes. No idea how to visualize anything beyond 3d.

Here's a cool article:

Wikipedia -- Hilbert space

(February 22, 2022 at 9:27 pm)Fireball Wrote:

(February 22, 2022 at 8:48 pm)arewethereyet Wrote: Doesn't a circle imply that there's the same radius all the way around?

Yes. In geometry, we define a circle as "the set of all points in a plane that are equidistant from a given point, called the center of the circle". The question posed by the OP shows ignorance of this basic concept.

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.

(February 23, 2022 at 10:34 am)polymath257 Wrote:

(February 22, 2022 at 9:27 pm)Fireball Wrote: Yes. In geometry, we define a circle as "the set of all points in a plane that are equidistant from a given point, called the center of the circle". The question posed by the OP shows ignorance of this basic concept.

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.