Re: The Circles

On 7/1/2025 2:02 PM, sobriquet wrote:

Op 01/07/2025 om 13:29 schreef sobriquet:

Op 01/07/2025 om 07:16 schreef Ross Finlayson:

On 06/30/2025 11:29 AM, Chris M. Thomasson wrote:

On 6/28/2025 8:38 PM, Ross Finlayson wrote:

Oh, been a while, figure I'll post.

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An ellipse is nothing more than a circle projected in 3d? ;^)
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That's frivolous.
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An ellipse is constructible from a loop of string and two pegs.
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An image of a circle onto a plane as projected from
an incident angle via 3D:  is not an ellipse, either.
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Ask your shadow.
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Looks like an ellipse to me:
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https://www.desmos.com/3d/syqqdp9cef?translucentSurfaces

 Uh.. slight fix:
 https://www.desmos.com/3d/om4r4nmoeg?translucentSurfaces

Yup. There is a circle in there. I think that any 2d ellipse, degenerate or not, has a 3d counter part of a unique circle rotated in 3d and projected. A degenerate case would be a line segment, looking at a CD on edge perhaps, for an analogy. Well, take the mid point and radius of the segment. Draw a circle with center of the mid point via compass. That is it's "hidden" circle in 3d counterpart being rotated in a sense?