Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Education » math-teach

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
kirby urner

Posts: 1,779
Registered: 11/29/05
Re: Visualiing Derivatives with Cubes
Posted: Sep 1, 2013 5:51 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply
att1.html (2.5 K)

Lots of ways to delta a shape by a little bit. Any delta you indicate as a
change in volume in something may be modeled cube-wise or tetrahedron-wise
or some other.

But it's not my agenda to replace the cube across the board. That's an
agenda that gets projected by the cube-insecure.

Lets say calculus is what it is with its cubes and squares.

What I'm into this days, long with Koski, is the scissoring rhombuses,
sharing an axis, evolved from the "two book covers" thought experiment
(each book cover 60-60-60 and kept open to on-another at 180 degrees -- a
page flaps back and forth).

Keeping 5 edges equal and changing just one, that's what interests me. We
use that program for getting volume from edges as inputs. I had a link to
edu-sig for the Python code.

Whether there's some cool "tetrahedron calculus" in the pipeline I wouldn't
necessarily know. The branch of math I've been talking about is fairly
populous.

Zubek keeps repeating a few names but there are more. I don't know what
everyone is up to, don't make it to all the conferences (like the SNEC ones
-- I was in of the founders of SNEC, more so Russell Chu, and see Chris in
Philadelphia maybe once a year).

Kirby

in Chicago



On Sun, Sep 1, 2013 at 11:37 AM, Joe Niederberger
<niederberger@comcast.net>wrote:

> Its easy to visualize what's going on with the derivatives of x**2 and
> x**3 with the usual square and cube representations of those functions: a
> square can be enlarged by "building out" along two edges, a cube can be
> likewise by "building out" on three faces -- the "error" artifacts are the
> little dx corner square in the 2D case, the corner cube as well as the
> three edge "lines" in the 3D case. Its just a cute way of seeing where the
> derivatives d/dx(x**2) = 2x, and d/dx(x**3) = 3(x**2) come from.
>
> But I don't see how to do anything similar with triangles or tetrahedrons.
> Perhaps Kirby will show us. Or does this simple exercise point to something
> a bit more fundamental than simple "cultural choice"?
>
> Cheers,
> Joe N
>




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.