hey guys..
just wondering how you guys do the torus questions.
by slicing or cylindrical?
the arnold book uses cylindrical and its a bit confusing I think.. especially cause they leave out a lot of lines. (well it is to me ok? )
and then i found these other notes that do it by the annulus way.. and end up with (x1 - x2)(x1 + x2)
but it seems to only work if the circle that you're rotating, doesn't have the centre at (0,0).
because if it is at the origin, (x1 - x2) ends up being zero... so the
pi(x1-x2)(x1+x2) method doesn't work.
any suggestions?
well i tried doing the annulus way to answer this...
'the circle x^2 + y^2 = 25 is rotated around the line x = 10. find the volume of the torus found'
answer is 1000 pi ^2 or 500 pi ^2 sorry i'm having a mental blank and can't remember it exactly.. will edit post when i go and check.
just wondering how you guys do the torus questions.
by slicing or cylindrical?
the arnold book uses cylindrical and its a bit confusing I think.. especially cause they leave out a lot of lines. (well it is to me ok? )
and then i found these other notes that do it by the annulus way.. and end up with (x1 - x2)(x1 + x2)
but it seems to only work if the circle that you're rotating, doesn't have the centre at (0,0).
because if it is at the origin, (x1 - x2) ends up being zero... so the
pi(x1-x2)(x1+x2) method doesn't work.
any suggestions?
well i tried doing the annulus way to answer this...
'the circle x^2 + y^2 = 25 is rotated around the line x = 10. find the volume of the torus found'
answer is 1000 pi ^2 or 500 pi ^2 sorry i'm having a mental blank and can't remember it exactly.. will edit post when i go and check.