Best books on nomography ?

[Leif]

I'm interested about nomography books. I have bought quite many of them, but many of them are not very mathematical and most of them discusses same topics. The book "Otto: Nomography" is an exception and it discusses also some mathematical tricks to make determinants and criteria for nomography. The book is from 1963 and is a translation from polish.

Does anyone know a still better discussion about nomography and theoretical nomography ? It seems that art of nomography stopped totally after sixties. I have found nomographs extreme useful in some cases. I use PyNomo to make nomographs.

\leif

[Glen]

I'm interested about nomography books. I have bought quite many of them, but many of them are not very mathematical and most of them discusses same topics.

I only own a couple (of which I can only find one at present), but I have read several more. Most of them indeed discuss the same topics, and at a very nontechnical level

The book "Otto: Nomography" is an exception and it discusses also some mathematical tricks to make determinants and criteria for nomography. The book is from 1963 and is a translation from polish.

I think the Otto book is probably the best overall book that I have read, but some other books cover occasional topics Otto does not. If I had to choose only one book on nomography, I think I would choose Otto's.

As an example of other books with information I hadn't seen
elsewhere, Davis' book:

Nomography and empirical equations.
Author: Davis, Dale S. (Dale Stroble), 1901-
Title: Nomography and empirical equations. 2d ed.
Publisher: New York : Reinhold Pub. Corp, [1962]
Description: 261 p. : illus ; 24 cm.

has a number of ideas I hadn't seen before.
I don't own this book; I should go reread it (the university library has it).

Does anyone know a still better discussion about nomography and theoretical nomography ? It seems that art of nomography stopped totally after sixties. I have found nomographs extreme useful in some cases. I use PyNomo to make nomographs.

I only found the PyNomo site earlier today.

I know a few other people who are into nomography. I will point some of them here.

Have you seen Winchell Chung's pages?
e.g. http://www.projectrho.com/nomogram/standardForms.html

He has an extensive bibliography, with short reviews of many of the books: http://www.projectrho.com/nomogram/reading.html

It is my understanding that Winchell has written a fair bit of nomography code as well.

[Ken Burnside]

I'm not a mathematician. Nor do I play one on TV.

I do publish games with nomograms, and am ALWAYS looking for easier ways to generate them.

[Leif]

Have you seen Winchell Chung's pages?
e.g. http://www.projectrho.com/nomogram/standardForms.html

He has an extensive bibliography, with short reviews of many of the books: http://www.projectrho.com/nomogram/reading.html

It is my understanding that Winchell has written a fair bit of nomography code as well.

After reading projectrho pages about nomography I started to order books and got into graphical computation.

Recently I found a blog article about nomography:

http://myreckonings.com/wordpress/2008/ ... ic-design/

\leif

[Glen]

Recently I found a blog article about nomography:
http://myreckonings.com/wordpress/2008/ ... ic-design/

I hadn't seen that one before. Thanks.

[joe marasco]

The following books are listed in no particular order. They have been accumulated over the years and are my “hard copy” library on the subject.

1. d’Ocagne, Maurice: Traité de Nomographie, Paris, Gauthier-Villars, 1899; 480 pages
The classic work, in French, by the inventor of the method. Comprehensive. Obtained at significant cost from a French antiquarian book dealer.

2. d’Ocagne, Maurice: Le Calcul Simplifié, translated by Howlett and Wiiliams
Subtitled: Graphical and Mechanical Methods for Simplifying Calculation
MIT Press, Charles Babbage Institute Reprint Series for the History of Computing
Translation of the third edition, 1928. ISBN 0-262-15032-8
A disappointment: only one short chapter on nomographs. But perhaps the only example of d’Ocagne in English.

3. Davis, Dale S: Empirical Equations and Nomography, New York, McGraw-Hill, 1943; 200 pages
About 60 pages on nomographs. Nicely done, lots of examples. Very terse style.

4. Brodestsky, S: A First Course in Nomography, London, G. Bell and Sons, 1920; 135 pages
A very “gentle” introduction to the subject, assuming a minimum of previous experience with mathematics. Lots of examples. Less useful once the basics are understood.

5. Mavis, F.T.: The Construction of Nomographic Charts, Scranton, International Textbook, 1939; 132 pages
A very good “second book” on the subject. Begins immediately with the determinant approach. Not a good place to start if you have not had any previous exposure to linear algebra and systems of equations.

6. Levens, A.S.: Nomography, New York, John Wiley and Sons, 1948; 176 pages
My favorite. Breaks the subject down into classes of nomographs, which is very similar to what Leif Roschier has done on his PyNomo web site. Very detailed explanation of construction of each type. There is a chapter on the determinant approach at the end of the book. Many beautiful examples

It was also common in the 1950’s to include a chapter on nomography in technical drawing textbooks. For example, see:

7. Giesecke, Mitchell, and Spencer: Technical Drawing, New York, MacMillan, 1958; Pages 623 – 640.

I hope this helps. These books may be hard to obtain; I would start with AbeBooks: http://www.abebooks.com, and do a search on the keyword "nomography".

[joe marasco]

With respect to item 6 in the previous post, please note that there is a second edition of Levens' book, variously given as 1959 or 1965, which has 296 pages. I have ordered a copy and will report on the differences between the two editions once I get a chance to compare them.

Thanks.

Joe

[Leif]

I own Levens:Nomography, second edition, second printing (May 1965). Joe has is right. Levens' book has been inspiration and source in some blocks. I found geometrical approach to be most straight forward way especially in N/Z-nomograph.

This is one of my favourite books and very cheap. Few dollars at abebooks.com

\leif

[pmartel]

The following books are listed in no particular order. They have been accumulated over the years and are my “hard copy” library on the subject.

1. d’Ocagne, Maurice: Traité de Nomographie, Paris, Gauthier-Villars, 1899; 480 pages
The classic work, in French, by the inventor of the method. Comprehensive. Obtained at significant cost from a French antiquarian book dealer.

2. d’Ocagne, Maurice: Le Calcul Simplifié, translated by Howlett and Wiiliams
Subtitled: Graphical and Mechanical Methods for Simplifying Calculation
MIT Press, Charles Babbage Institute Reprint Series for the History of Computing
Translation of the third edition, 1928. ISBN 0-262-15032-8
A disappointment: only one short chapter on nomographs. But perhaps the only example of d’Ocagne in English.

3. Davis, Dale S: Empirical Equations and Nomography, New York, McGraw-Hill, 1943; 200 pages
About 60 pages on nomographs. Nicely done, lots of examples. Very terse style.

4. Brodestsky, S: A First Course in Nomography, London, G. Bell and Sons, 1920; 135 pages
A very “gentle” introduction to the subject, assuming a minimum of previous experience with mathematics. Lots of examples. Less useful once the basics are understood.

5. Mavis, F.T.: The Construction of Nomographic Charts, Scranton, International Textbook, 1939; 132 pages
A very good “second book” on the subject. Begins immediately with the determinant approach. Not a good place to start if you have not had any previous exposure to linear algebra and systems of equations.

6. Levens, A.S.: Nomography, New York, John Wiley and Sons, 1948; 176 pages
My favorite. Breaks the subject down into classes of nomographs, which is very similar to what Leif Roschier has done on his PyNomo web site. Very detailed explanation of construction of each type. There is a chapter on the determinant approach at the end of the book. Many beautiful examples

It was also common in the 1950’s to include a chapter on nomography in technical drawing textbooks. For example, see:

7. Giesecke, Mitchell, and Spencer: Technical Drawing, New York, MacMillan, 1958; Pages 623 – 640.

I hope this helps. These books may be hard to obtain; I would start with AbeBooks: http://www.abebooks.com, and do a search on the keyword "nomography".

Sorry to be late to the party. I would recommend
Adams, D.P. : Nomography Theory and Application, Archon Books, 1964

Best wishes,
--Phil Martel

[joe marasco]

The Douglas P. Adams book "Nomography Theory and Application" has become expensive in the used books aftermarket. However, I found a web site that allows you to download it in pdf format for free. That link is: http://www.addebook.com/tech2/mathemati ... _5405.html.

It is probably worth your time and effort to at least preview the book in this way before spending upwards of $75 to buy a copy.

Thanks.

Joe

[Leif]

Thanks Joe for the link!

I somehow can not find the pdf on the page. Should I register or is this (again) issue that users outside U.S. can not download content based on difference laws on copyright span?

\leif

[joe marasco]

Lee Johnson's book:

http://www.amazon.com/Nomography-Empirical-Equations-Lee-Johnson/dp/0471444847/ref=sr_1_1?s=books&ie=UTF8&qid=1356294399&sr=1-1&keywords=Lee+Johnson+Nomography

http://www.bookfinder.com/search/?ac=sl&st=sl&ref=bf_s2_a1_t1_1&qi=FXl9SQa2ZmtR2vYnpTvfq5fXdB4_9895181894_1:3:5&bq=author%3Dlee%2520h%2520johnson%26title%3Dnomography%2520and%2520empirical%2520equations

I got a used copy in reasonable condition for not too much money. This is a good book, reminding me how textbooks used to be written: Crisp, to the point, no bloat, and lots of great insight. Although it is an introductory treatment—no determinants—it is a good one. His scheme for construction is consistent throughout, and he goes through the basic forms very well. What I particularly liked was his discussion of alternative presentations, showing how some layouts would be prone to fewer usage errors than others. He also has a great discussion of the effect of design on the relative errors in reading the results, and the propagation of error effects when there are multiple isopleths and pivot lines.

The second half of the book on fitting empirical equations is quite dated, on the other hand. Even twenty five years ago we were doing least squares fits on pocket calculators that had that function programmed in.

Nonetheless, worth the money, and highly recommended if you are introducing someone new to the subject.

[Glen]

Thanks Joe,

I'm interested in the material relating to such 'usage error' in nomography, from the point of view of measuring and reducing it, and also in the sense that it gives a bound on the accuracy with which there's any point in approximating a relationship with a nomographic relationship.

In particular, dealing with questions like - "If I can get a maximum relative error of 0.42 percent on a parallel-scale nomogram, given the size of the error in using one with a curved scale, is there much point in pursuing the theoretically-better-approximation to the function?". Such calculations give us a better idea of 'when to stop' with approximate nomography, which is what I am working on at the moment.

So your mention of Johnson is particularly interesting.

I have a couple of papers by Lyle that discuss the issue a little but I'll keep my eye out for Johnson, thanks.