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An ostrich egg is classified as an ellipsoid and if we spin it around it's major axis it's classified as a prolate but my fried is arguing that we can not spin that ellipsoid around its minor axis because then "it won't be symmetrical around the axis" and this has confused me.

Basically I want to know if the same ellipsoid rotated about minor axis that was categorized as oblate, can also be categorized as prolate when we rotate it about the major axis.

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    $\begingroup$ You really must read Wiki more carefully and quote it accurately. It says that if one rotates an ELLIPSE about its major/minor axis then one gets a prolate/oblate spheroid. $\endgroup$
    – ancient mathematician
    Commented Jun 3 at 13:56
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    $\begingroup$ Well prolate doesn't change into oblate: they're two distinct 3-d shapes we get by rotating the 2-d ellipse about different axes. $\endgroup$
    – ancient mathematician
    Commented Jun 3 at 16:53
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    $\begingroup$ It's not the same ellipsoid. That's the fundamental issue of this discussion. A prolate ellipsoid is a prolate ellipsoid, an oblate ellipsoid is an oblate ellipsoid, and an ellipse is not an ellipsoid at all. $\endgroup$
    – David K
    Commented Jun 4 at 3:12
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    $\begingroup$ All this talk of turning prolate ellipsoids into oblate ellipsoids makes the same kind of sense as turning a Toyota into a Volkswagen by building it in Germany instead of Japan. In reality, you simply don't change Toyotas into Volkswagens, even though they are both cars. There's a company that build Toyotas, and there's a company that builds Volkswagens. $\endgroup$
    – David K
    Commented Jun 4 at 3:18
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    $\begingroup$ @mr_e_man How do you get "different perspective" from "spin that ellipsoid around its minor axis"? The question is simply nonsensical, that's all. We can try to guess what OP had in mind when asking it, but only OP knows and they have not yet clarified their meaning sufficiently. OP says, "So if we have an ellipsoid. When we rotate that ellipsoid along the minor axis it's called an oblate." Perhaps if OP would actually quote verbatim from some source from which they got these words, we'd be able to explain what the words actually meant and how to assemble them into a meaningful statement. $\endgroup$
    – David K
    Commented Jun 25 at 17:43

2 Answers 2

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Forget about spinning. An ellipsoid has three perpendicular axes; it can be constructed from a sphere, by stretching it along these axes. The stretch factors may or may not be equal.

It's called a spheroid if two axes are equal. It's prolate if the two equal axes are shorter than the third axis. It's oblate if the two equal axes are longer than the third axis. They cannot both be true at the same time.

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    $\begingroup$ Notwithstanding our contretemps in comments under the question, I agree with this answer completely and find it useful. It has the advantage over other explanations in that it avoids the language that appears to be confusing the question-asker. +1 $\endgroup$
    – David K
    Commented Jun 25 at 17:57
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An ellipse will make two differently shaped ellipsoids when revolved around its minor vs. major axis unless it is a circle, in which case it will create a sphere in both cases. So yes, it can form a prolate spheroid by revolving around the major axis and an oblate spheroid by revolving around the minor axis, but the two ellipsoids will not be congruent as long as the major axis is longer than the minor axis (i.e. it's not a circle).

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