Re: More complex numbers than reals?

On 7/21/2024 4:22 PM, Moebius wrote:

Am 22.07.2024 um 01:01 schrieb Chris M. Thomasson:

On 7/21/2024 3:57 PM, Chris M. Thomasson wrote:

 

Also, from the unit circle, all circles and ellipses can be created. The ellipse aspect is that of a circle rotated in 3d is an ellipse when viewed on the projected plane. Check this out in VR:
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https://skfb.ly/6RozT

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Think of a circle in 3d. Looking at it dead on as a circle. Then, change the camera view. It becomes an ellipse.

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A screenshot:
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https://i.ibb.co/BcX7yQW/image.png

 It's clear that you are a "visual type". :-P

Yeah! :^) From any 2d ellipse we can create its circle. Say a ellipse with an origin point and a radii. For a spheroid, take the unit sphere:
vec3 origin = { 0, 0, 0 }
vec3 radii = { 1, 1, 1 }
For a unit circle, say in the x, y plane:
vec3 origin = { 0, 0, 0 }
vec3 radii = { 1, 1, 0 }
Looking down the z axis it would appear as a unit circle.
For an ellipse in the x, y plane:
vec3 origin = { 0, 0, 0 }
vec3 radii = { 1, .5, 0 }
These can all be plotted parametrically. The fun part is that a circle
 From any circle we can view it in a 3d realm such that it can create any ellipse? Fair enough?