Color Plate 3 at:
http://www.rwgrayprojects.com/synergetics/plates/figs/plate03z.html
shows that physical models can not just inspire but can also be used to
derive and prove things by construction.
I haven't read any other books that use physical models that you could
hold in your hands to derive or prove things.
I think the coordinate system to use for color plate 3 is at:
http://mysite.verizon.net/cjnelson9/index.htm
and
SynergeticsApplication7.nb (2 MB) - Mathematica Notebook at:
http://library.wolfram.com/infocenter/MathSource/600/
Are there any examples of proofs with 3D contraptions or physical models
or are all mathematical proofs of theorems paper and pencil proofs?
Cliff Nelson
Dry your tears, there's more fun for your ears,
"Forward Into The Past" 2 PM to 5 PM, Sundays,
California time,
http://www.geocities.com/forwardintothepast/
Don't be a square or a blockhead; see:
http://mysite.verizon.net/cjnelson9/index.htm
http://library.wolfram.com/infocenter/search/?search_results=1;search_per
son_id=607
Androcles - 26 Jul 2008 16:10 GMT
| Color Plate 3 at:
| http://www.rwgrayprojects.com/synergetics/plates/figs/plate03z.html
[quoted text clipped - 16 lines]
| Are there any examples of proofs with 3D contraptions or physical models
| or are all mathematical proofs of theorems paper and pencil proofs?
Such have been around since Pythagoras.
Make four copies of the same right triangle, arrange in a square and
prove a^2 + b^2 = c^2.
Here is a physical model of Einstein's relativity, derived and proved:
http://www.androcles01.pwp.blueyonder.co.uk/Smart/LT.gif
For the algebra see
http://www.androcles01.pwp.blueyonder.co.uk/Smart/Smart.htm