Re: The Circles

On 07/06/2025 04:33 PM, FromTheRafters wrote:

on 7/6/2025, sobriquet supposed :

Op 06/07/2025 om 15:13 schreef Ross Finlayson:

On 07/01/2025 04:29 AM, sobriquet wrote:

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

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That's like AP and his ovals.

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Can you be specific? Are you denying that this is an ellipse?
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y^2 + 2*sqrt(2)*x^2 = 1
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Or are you claiming that this is not the shape you get when you
project a unit circle (centered on the origin) in a plane z =
sqrt(2)*x onto the z=0 plane?
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There are ellipsoids of various sorts,
and as for oblate spheroids, what "a
traditional section of conics, ..., and
a flashlight through it projected onto
various surfaces", may result.
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..., And the entire modern mathematical problem
of elliptic curves and elliptic curve cryptography
is broken by a guy with a sufficiently large setup
of conic sections and flashlight and backdrop.
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Or, "they should've known, AP warned them."

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Elliptic curves have little to do with ellipses, they are third degree
equations. Not much to do with conic sections at all.

Oh, what if you project them all the way down the axis?
Modular fields of Galois 2, ..., posh.
Notice the shadow of a ball on the ground, it's not an ellipse
except when all the heavens align to put you at the monocular
point at infinity and then you can't see it anyways.
"Behind the noodles...", as it were.