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In the following answer answer ,

Euclid's right-angle postulate excludes the existence of cone points: right angles at the vertex of a cone are smaller than right angles elsewhere on the cone. So this postulate cannot be proved insofar as the other axioms apply on a cone, which one could argue that they do.

Similar to one of the other commenters on that post, I too am having difficulty in visualizing this statement. I am looking for an answer which can explain the above pictorially , as I couldn't find any pictures on google images illustrating the idea above.

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A cone can be formed by joining the straight edges of some circular sector made out of paper. If a right angle is drawn on the flat sheet at the vertex before joining the edges, then when the cone is formed the angle may not be right anymore in 3D space.

Indeed, from the perspective of differential geometry angles cannot be defined intrinsically (from the persepective of an ant that is stuck to the surface) at the cone vertex.

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  • $\begingroup$ "A cone can be formed by joining the straight edges of some circular sector made out of paper. " proof? $\endgroup$
    – Cantor Dust Drachen
    Commented Jun 19, 2021 at 13:52
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    $\begingroup$ @Buraian Why don't you try it yourself? $\endgroup$
    – Parcly Taxel
    Commented Jun 19, 2021 at 13:56
  • $\begingroup$ I would but I Feel I don't have enough background to do it, my geometry is rather weak. If you could link to a proof that also would be appreciated. $\endgroup$
    – Cantor Dust Drachen
    Commented Jun 19, 2021 at 13:57

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