It seems like I am not the only one interested in astrolabes. I am very interested in Mr. Morrison’s book as well. I have emailed him to see if he has a pdf version of his book. I know these have been posted a long time ago but wondered if you still had the AutoCAD of the astrolabe. I am very excited about this old technology and am interested in if you have any additional information that I would like to take a look at. Thank you in advance for your time.

Best Regards,
Nick Trudeau

Thank you for your comment, Luiz. It’s nice to hear from teachers who are interested in (re-)introducing nomograms to students. I’ve gathered together several articles on the use of nomograms in electrical engineering (well, most of them are standard nomograms, anyway) that you and your students might find interesting. You can download a zip file of them from

Unfortunately, despite my best efforts to not break a two-year tradition, I simply couldn’t get a calendar together by the end of the year. I’ve been involved in multiple projects related to the blog as well as other family matters, and the deadlines just didn’t allow it. I’ll be starting to work soon on one for next year, though. It’s a niche thing about my blog that I like. Thanks for the compliment, though! — Ron

The factor to the small-amplitude period for larger amplitudes can be written as a rational a/b where a = 6303 + c and b = 6303 - 11c and c =(w/10)^2, amplitude w in degrees! The formula is found by writing the factor as a continued fraction and then evaluate.

Really! I didn’t know that. I know that rational expressions are very powerful tools in analysis, much more capable of fitting curves than polynomials, but I hadn’t encountered this factor for large pendulum amplitudes. This is very interesting to me—thank you very much! — Ron

Over the years searching for ways to do nomographs I have never come across to an article as excellent as this one. As part of my daily work I work on a particular nomograph almost every day and I have been looking for a way to execute my work without ever reading this nomograph but to no avail (see link below).

https://docs.google.com/open?id=0B-UXy3wQpIlXNTNhMjI2NjQtNjY5OS00MTAwLWI0NGItMDE3MDMyYThmZTI5

To read the nomograph you need the diameter and internal pressure to obtain plate depth.

Your assistance will be appreciated.

Regards
Tshepo

For others who might be interested in this subject, I sent Tshepo a write-up including a derivation and a Python script for calculating the results of the nomogram quite accurately over the tests I ran against it. Swanson provides the sequence of equations he used for designing his initial range from 100 to 600 psi, but there are significant differences outside this range that required measurements off the nomogram and equations curve-fitted to the data. The two of have just started to look at this, but if you are interested in getting the current preliminary version, feel free to email me at ron “at” myreckonings.com — Ron

This looks fantastic and I’d really love to try it out, but…

I’ve never used Python before. I downloaded and installed Python, MiKTeX, and all the prerequisite packages/modules, along with PyNomo itself. I can’t get any of the examples to work. I keep getting an error that “close_fds is not supported on windows”. It seems from the Traceback that the problem might be with PyX. Have you any idea how I might resolve this, or where I might find someone who can?

I can send a screengrab of the command window to anyone who’s interested enough to help.

Thanks.

Hugh and I corresponded on this problem right after this comment, and we independently solved the problem. When installing the necessary support packages for PyNomo, the older version 2.6 of Python needs to be installed and also the older version 0.10 of the PyX package. I’ve now updated the essay above to include a link to a PDF file of very detailed instructions on installing PyNomo and the other required packages on a Windows XP or Windows 7 PC, with a helpful addition from Hugh in one section. Thanks, Hugh! — Ron

Thank you! As I mentioned somewhere else, I somehow never encountered any nomograms until the late 90’s when I saw simple versions of them in a couple of articles on sundials. When I eventually started researching them several years later for these essays, I was blown away with what I found. I still collect articles and books on nomograms, and I have many more interesting ones to share in future essays. I’m also actively involved in creating new nomograms for projects and journal articles, so my interest has only increased in these things. Thanks again for your nice comments, John. — Ron

I am back after a long absence _____other activities pull one away. About this bit : ” The study of lightning calculators of the past is a fascinating one for me from a mathematical aspect more than a psychological one. We’ve seen years of articles by educators bemoaning the dependence of students on calculators, but I see little in school textbooks on mental math other than simple estimation. And yet when I have presented basic methods of mental calculation to classes (elementary and college), I’ve met with incredible interest. Certainly the BrainMan documentary is a very popular one. But these types of presentation generally ascribe abilities in these areas to mysterious machinations in the minds of remote geniuses, which makes for a good story but can be discouraging. In fact, these individuals through talent and training acquired a knack for racing headlong through calculations that are not mysterious at all once the methods are taught.

And they are not being taught. Mental calculation can be a highly creative and satisfying endeavor offering a variety of interesting strategies, more than I have presented here and many more than most people realize. It is a skill that engages both children and adults, and one that naturally leads to a real familiarity with the properties and relationships of numbers. It provides a useful and fun approach for developing a number sense and generating a true appreciation for the elegance of elementary mathematics. It should not be a neglected art. ”

There are 2 points worth informing you about. ONE : When you describe the fantastic abilities of the brilliant mental calculators , it over-awes the common plodders , like me.

TWO : i have been chasing this * mental maths* for donkey’s years. The major problem is ** HOW TO HOLD the INTERMEDIATE NUMBERS IN ONES HEAD , while doing, for instance , the squares of 3 and 4 or 5 figure numbers. !!
Further, i have taught mental maths by going to a local school. Yes, the kids are very eager to learn. They do pick up our mental ,quick calculation methods. HOWEVER, the maths TEACHERS are too OLD ( mentally) to learn our methods. ERGO, no follow up work is done in the regular mathematics classes in the use of the mental ,quick methods. Alas , it , thus remains just a curiosity.

Not the kids, but their teachers need to be taught these methods.

I do teach maths ( Calculus etc) at home to students every evening, 3 pm to 7 pm_____but that’s my hobby not my profession.

Just a heads-up because I’m working on a presentation about Heaviside and looking for examples of his operator method, and your site comes up pretty high in the search rankings.

ty very much.

Based on someone else’s question I received by email, the problem could lie with dealing with the parentheses. For example, in the term 5(40(0)+42) of Example 1, the innermost parentheses are calculated first. The order would be 40(0) = 0, then 0 + 42 = 42, then 5(42) = 210. Then

Hi Tom. Thanks for your comment–I had never heard of this concept. I found that chapter of Needham’s book on one of his Visual Complex Analysis pages on the University of San Francisco website at http://usf.usfca.edu/vca//PDF/amplitwist.pdf

Nice to hear from you again, Scott! Thanks for your comment. — Ron

Could you please help me. I’m busy installing a wireless weather station and I need to point the wind sensor to true north. I have a compass (360° being magnetic north), but how many degrees left or right of magnetic north is True North?

I am in Nelspruit, 25° 30’01. 73” S and 30° 59’32. 10” E . Elevation - 804m

Thanking you

Thomas Barry

There is a good website to find the magnetic variation (sometimes called magnetic deviation as in this website) for any location in the world:

Shame I missed it for this year. Will there be a 2012 edition?

Thanks for asking! I may resurrect it for 2012, as I haven’t had time to create a new calendar for next year. I’ll see, and if I do I’ll email you and let you know. — Ron

Thank you, Rik. I read Trachtenberg’s book years ago, and Ramanujan is rightly considered a genius who died way too young. — Ron

I just wanted to mention that as a materials scientist myself, I use ternary plots all the time. They’re absolutely critical to some aspects of work with ternary atomic systems. My current work is in CuInSe_2, a solar material. We characterize our grown thin films (physical vapor deposition) with a scanning electron microscope (SEM) that has energy dispersive spectroscopy (EDS) for characteristic x-rays (given off by the thin film compound). The atomic % calculated by the absorbed characteristic x-rays are then plotted on a ternary plot to show us how much of each atom is in the film (assuming we don’t have contaminants etc.). Then of course phase-lines are added to the plot sometimes to show where critical regions of certain phases exist.

As a graduate student I usually ask any incoming undergraduate laboratory help to first plot ternary plots of the compounds we grow from our data. It’s always interesting to see how they come up with solutions to the problem of what is a somewhat non-standard plot for the rest of the world.

Excellent blog and post!
-Allen

Thanks, Allen. This is a very nice example of the use of ternary plots in the modern world. I can imagine how odd it must seem to new students. I’d really like to see one of your plots if you don’t mind emailing me an example. — Ron

You’re right, my mistake–I’ll edit my text to correct this. Thanks for clarifying this, Nicky! — Ron

Know of any such thing. I made one, but why..?

thanks

rhh

Note: Richard and I have been emailing back and forth about this since he submitted this comment, and I have been unable to find an example of a nomogram for Heron’s equation. The best I can find are nomograms based on the A=(1/2)bh formula, which of course yields a simple multiplication nomogram. Meanwhile, Richard has sent me his example of a nomogram in intercept chart form for this problem, and has graciously offered it for inclusion in a future blog post I am planning. — Ron