There always exists a circle such that, given any three non-colinear unique points in 3-space, all three points lie on the border of that circle. Spherical geometry is not required.
A fair point. The important part is the last bit, which points out that spherical geometry is not a requirement for it to hold, which is the only reason I replied to you in the first place
Readers added more context: Any three unique points on a sphere form a circle.
There always exists a circle such that, given any three non-colinear unique points in 3-space, all three points lie on the border of that circle. Spherical geometry is not required.
No, three unique points in 3d space that are colinear will not form a circle.
Thank you! Edited.
But now you’re just repeating the post lol
A fair point. The important part is the last bit, which points out that spherical geometry is not a requirement for it to hold, which is the only reason I replied to you in the first place
Yup, a circle that lies on the surface of the sphere. You’re only safe underground or in space.