## Multiple scales on one curve

Mathematics about graphical computing
Glen
Posts: 67
Joined: Fri Jan 25, 2008 4:11 am
Location: Australia

### Multiple scales on one curve

In the Literature section, Leif pointed to a series of online articles (blogposts seems too lame a word for these glittering gems) by Ron Doerfler. The third of them:
[url]http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-iii-transformations/[/url]

says the following:

[quote]There are non-projective transformations as well that can be used to create nomograms in which all three scales are overlaid onto one curve (although the third will have different tick marks). This is highly mathematical and involves things called Weierstrassâ€™ Elliptic Functions, so Epstein is a resource if there is interest in the details. Epstein provides nomograms of this sort for the equation u + v + w = 0 (which can be generalized to any equation of this form, including ones in logarithms).[/quote]

I've never seen Epstein's book. Has anyone here seen it? How does this work?
Leif
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I don't know or own the book (yet). Ordered it in order to find out...
http://www.abebooks.com/servlet/SearchR ... y&x=55&y=9

\leif
RonDoerfler
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Hi All,

I've looked more into using Weierstrass' Elliptic Functions to create a nomogram, and I've posted an essay with the details:

http://myreckonings.com/wordpress/2008/ ... -nomogram/

Ron
Leif
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Joined: Mon Dec 31, 2007 3:03 pm
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### Re: Multiple scales on one curve

RonDoerfler wrote:Hi All,
I've looked more into using Weierstrass' Elliptic Functions to create a nomogram, and I've posted an essay with the details:
http://myreckonings.com/wordpress/2008/02/24/a-zoomorphic-nomogram/
Ron

Nice nomogram with a combination of art and math !

Glen wrote:I've never seen Epstein's book. Has anyone here seen it? How does this work?

It is stated, according to Epstein, that only nomogram of type

f(u)+g(v)+h(w)=0, (1)

is capable of nonprojective transformation. This is proved by Gronwall in 1912 in paper that I do not own.

If I understand correctly, Eqs, (1) may be put into "circle and line" -form, where circle represents two parameters, or into "Weierstrass"-form as is the fish nomogram made by Ron, where all parameters are in the single axis. In terms of practical engineering problems, I wonder have these nomograms been used in practice ?

\leif