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Volume of elliptic torus (help)
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The slider (beta) between i.e. 45 and 60 degs determines a strip embedded by two ellipses. My request deals with the chance to compute the shown area (PP'Q'Q) and the volume of intercepted torus. Thanks in advance.
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excuse, the external likeelliptic curve is not an ellipse
Never mind! The differences of w in the middle are very slight and don't make any trouble for my purposes. Unfortunately your proposed solution (parametric way, a couple of weeks ago) is unsuitable, due to intersect linecurve failure. Thx
To be precise, only one line performs the interception. Cheers
Probably the post title is erroneous, should be intended as elliptic ring, like shown in attachment. I beg your pardon, forum!
You basically need to integrate the area of the section over the interval in which the two generating functions revolve about the xaxis. Have a look at this reference, which deals with a similar problem: http://www.dm.unipi.it/syl/upload_doc/2230.INGAAnnalisaes8.pdf or have a look here for the basics about volumes of solids of revolution using the section method http://aulascienze.scuola.z...
in this post
https://help.geogebra.org/t...
your question is
not inside two normal lines to ellipse
sometimes you get that you ask it
I think that the volume you want is integral[w*(a(t)+b(t))/2,t,t0,t1] being a(t) the ellipse and b(t) the other curve
i tried with maxima
saludos
No!
Unfortunately too much details (mine) produce plenty of misunderstandings. Reference is made to the above comments. Sorry
Area of an ellipse having axes 2a and 2b:
pi*a*b
So, calculate the difference between the big ellipse and the little ellipse to get the area of the strip
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