OK, Imagine a circle drawn on a plane and you view the circle face-on. It looks like a circle.

Now imagine you tilt your view such that you view the circle along the surface of the plane. It looks like a line.

For every angle (0° <= x° <= 90°) at which you view the circle the circle will appear as an ellipse. Indeed, all possible ellipses will appear by this method.

Can this be used to find the circumference of an ellipse?

>>16724737 (OP)
>(0° < x° < 90°)*

Idk man. You can get circumference of elipse on zeozebra

>>16724762
Approximations.

>>16724737 (OP)
Isn't the circumference of the ellipse just [math]C_{ellipse}=C_{circle}*cos(θ)[/math]?

>>16724737 (OP)
>all possible ellipses
Can you prove that?

You should also notice something else, a circle rotation won't have an equidistant view to the observer.

>>16726614
It would work the same way that a unit circle can produce every right triangle.

>>16726675
Every right triangle can also be drawn in a rectangle. This doesn't prove the statements about the ellipse and it doesn't address the rotation does not map to an actual ellipse in the first place.
Adjusting a circle yaw puts one edge further back from you than the other and its furthest extents are not equal from the midline when viewed. What is the mathematical formula for squinting? I think mechfags call it tolerance.

>>16727044
Goddamn. I think you might be right. So the only real way to get all the elipses would not be yaw, but to compress or extend one side of the circle, and that's just giving it a major and minor axis, putting the concept back to square one.

>>16726614
>Can you prove that?
Yes. It's a projection of a circle.

>>16727069
You get them all with the projection.

>>16727234
>>16727235
https://math.stackexchange.com/questions/2388747/formula-for-ellipse-formed-from-projecting-a-tilted-circle-onto-the-xy-plane