Axes of Symmetry for Ellipsoid

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $\EE$ be an ellipsoid.

Then $\EE$ has exactly $3$ axes of symmetry:

the major axis of $\EE$
the mean axis of $\EE$
the minor axis of $\EE$.


Proof

From:

Major Axis of Ellipsoid is Axis of Symmetry
Mean Axis of Ellipsoid is Axis of Symmetry
Minor Axis of Ellipsoid is Axis of Symmetry

we have that these diameters of $\EE$ are in fact axes of symmetry.


It remains to be shown that there are no more.


This theorem requires a proof.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
To discuss this page in more detail, feel free to use the talk page.
When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.



Sources

Retrieved from "https://proofwiki.org/w/index.php?title=Axes_of_Symmetry_for_Ellipsoid&oldid=672665"