I am wondering how I can prove synthetically that the projection of a circle onto a plane is an ellipse.
2026-03-28 12:49:13.1774702153
Prove synthetically: projection of a circle onto a plane is an ellipse
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Realize the projected circle as the plane section of a cone with base the unprojected circle, ie., construct the cone.
Then either take it on belief that sections of a cone are the conic sections of plane geometry (ellipse is the only bounded one, so it must be that); or repeat Dandelin's proof for this cone and plane section.