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Topic: Visualiing Derivatives with Cubes
Replies: 9   Last Post: Sep 8, 2013 1:53 AM

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Joe Niederberger

Posts: 3,047
Registered: 10/12/08
Re: Visualiing Derivatives with Cubes
Posted: Sep 2, 2013 3:54 PM
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>I see no reason to suppose that this visualization would change. Whatever we take as the unit of area or the unit of volume, we would, sooner or later, need to show that the area of a rectangle is proportional to the product of its two dimensions, while the volume of a right parallelopiped
is proportional to the product of its three.

I was thinking along those lines. Of course you could keep your chosen unit and shape, but you'd be pushed into considering at least parallelograms and parallelepipeds
as the shapes that support visualizing the growth in a way that makes the derivatives plain. I didn't consider one would be forced to entertain right angles necessarily.

Cheers,
Joe N
 



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