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Commentary for "Solid of revolution about an oblique axis of rotation"

DreamWeaver

Well-known member
Sep 16, 2013
337
Excellent tutorial, Mark! Clear, concise, and above all, interesting... (Yes)


Just a though, mind, and it's a bit 'niche', as it were, but have you considered writing a little tutorial about how to work out the curvature, or radius of curvature of a function...?

It's a bit cheeky of me to ask, I'll grant you that (lol), but you do these things so well [sincerity].


All the best! :D

Gethin
 

Rido12

Well-known member
MHB Math Helper
Jul 18, 2013
715
Hi Mark! Very nice and clear derivation. Just a few questions:

Now, to obtain the projection of $dD$ onto $y=mx+b$, we find that by rotating everything by \(\displaystyle -\tan^{-1}(m)\), we may write:
$$\displaystyle du=dD\cos\left(\theta-\tan^{-1}(m) \right)$$
Why do we rotate by $-\tan^{-1}(m)$? And how does this obtain the projection?
 
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