Circles on Spheres

[SLD]

What is the relationship between the radius and circumference of a circle on a sphere? It’s not of course 2r. For a great circle it is 4r. But as the circle gets smaller it does get closer to 2r. Right? Which seems bizarre. But intuitive.

In hyperbolic geometry the circumference would be greater than 2r. But I can’t find any reference about a circle sphere.

SLD

 

[lpetrich]

That's an easy one. I'll make the sphere radius 1. Then, the circumference of a circle with radius angle r is 2*pi*sin(r).

 

[steve_bank]

Any circle on a sphere makes a solid angle from the center. Everything else falls out from that.

https://en.wikipedia.org/wiki/Solid_angle

 

[SLD]

That's an easy one. I'll make the sphere radius 1. Then, the circumference of a circle with radius angle r is 2*pi*sin(r).

Thanks. That makes sense. Measure the angle that the circle makes, not the distance along the surface from the center, which is secondary.

SLD

 

[Kharakov]

That's an easy one.

Thanks for letting us know this is easy. You still didn't solve my integer search....