(July 22, 2018 at 5:04 am)BrianSoddingBoru4 Wrote:Quote:As an example, take a flat surface, make a dimple on it. Trace an enclosed line, exactly equidistant from some other point on the surface as measured along the surface, and passing through the dimple. This line forms a perfect circle from the perspective of the surface.
I'm not being intentionally difficult, I'm seriously trying to grasp this.
On a flat surface, the circumference of a circle with a diameter of 10 cm would be 31.4 (ish)cm.
Ok, now we have a flat surface with a dimple. Let's say the dimple extends 1cm below (or above, doesn't really matter) the rest of the surface. We choose our centre point 5 cm from the dimple, giving us a radius of 5 and a diameter of 10. But the line marking the circumference of the circle would, when passing through the dimple, go down 1 cm then up 1 cm, making the circumference of this circle 33.4 cm, so C = pi x d wouldn't apply, making this not a perfect circle.
What am I missing?
Boru
A dimple is fine in 2D; but, how do we imagine such in 3D?
