- #1
IniquiTrance
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My textbook notes that if:
[tex]\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}}=1[/tex]
and [tex]a \neq b \neq c[/tex]
Then the ellipsoid is not a surface of revolution. It seems to me though that one can always find a curve in the plane, which when rotated around a line will produce the ellipsoid.
Why is this not true?
[tex]\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}}=1[/tex]
and [tex]a \neq b \neq c[/tex]
Then the ellipsoid is not a surface of revolution. It seems to me though that one can always find a curve in the plane, which when rotated around a line will produce the ellipsoid.
Why is this not true?