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

[MarkFL]

This topic is for comments/questions pertaining to:

http://mathhelpboards.com/math-notes-49/solid-revolution-about-oblique-axis-rotation-6683.html

 

[DreamWeaver]

Excellent tutorial, Mark! Clear, concise, and above all, interesting...


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!

Gethin

 

[Rido12]

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?