Date: Sep 1, 2013 5:51 PM
Author: kirby urner
Subject: Re: Visualiing Derivatives with Cubes
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
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).
On Sun, Sep 1, 2013 at 11:37 AM, Joe Niederberger
> 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"?
> Joe N