Guy Brandenburg's Web Page

Astronomy, telescope-making, math education.
Navigation (this page only)
Leon Foucault article
Amateur Telescope Making Workshop
Books on Telescope Making
Math on the Mall Field Trip
Books on math and science
Geometrix (geometry education software)
Chaos and Fractals
DC-area astronomy clubs
Astronomy links & resources
Math and Science Education Resources



  • Here is a link to the article in which Leon Foucault first described his original method of making silvered, parabolized, telescopic mirrors on  polished glass. I translated the article into English. As far as I know, mine is the only such translation. If you read the article, you will notice that Foucault's methods are not exactly the same as what modern-day optical workers know as the Foucault test. They also involve testing at the two foci of an ellipse, and also foreshadow what we call the Ronchi test.  Leon Foucault - original knife-edge article, in English
  • I run a weekly workshop under the auspices of the National Capital Astronomers (NCA) for making astronomical telescopes at the Chevy Chase Community Center (CCCC) in Washington, DC. It's every Friday evening from 6:30 to 9:30. attendance is free, and you only pay for materials. Follow this link for more details on this workshop:.  NCA/CCCC Mirror Making Workshop information  Why make your own telescope, when you can purchase one? Because you can make a BETTER one, for less money, too!  Why be an amateur telescope maker (an ATM)
  • Good, readable, step-by-step books on amateur telescope making (ATM).  Books on ATM
  • Here is a link to a field trip that I put together for my students at Alice Deal Junior High School in Washington, DC, called "Math On the Mall - And Beyond." I was fortunate to have had the enthusiastic cooperation of nearly 20 chaperones for over 100 students. I got the idea for my trip from the field trip for math teachers that Drs. Florence Fasanelli and Fred Rickey (and others) assembled over many years. On our trip, students and parents looked at a large number of things of mathematical and historical interest, even while walking to and from the subway. We also saw special exhibitions of original prints and drawings by M.C. Escher and rare old books and notebooks by Newton, Euler, Euclid, Banneker, and others, courtesty of the staff of the special collections libraries at the National Gallery of Art and  the Museum of American History We also saw many other things in and around the buildings on the National Mall and the Smithsonian Institution and National Gallery of Art. This is a large PDF file, 31 pages, 340 kB.     With this link, look near the bottom of the page    This is the PDF file itself.
  • Here is a link to a somewhat-annotated list of books on math and/or science. Look at this bibliography if you are a teacher or a student looking for something interesting to read in either field. It is broken down by subject area. In my 8th/9th grade algebra and geometry classes I have asked students  to read two of these books each year, and to write reports on them. Many of the results have been very good.  Brandenburg's list of Math, Science Books
  • I have been involved in a trans-atlantic geometry project known as  Geometrix. This is a piece of software that does just about everything that other dynamic geometry programs do, but it has two very important features that the other programs do not have: 
  1. First, in construction mode, it allows the teacher to pose a particular construction task for the student, and to give students feedback in real time (hints, suggestions, kudos) as they progress towards completing the construction The teacher can also specify what tools will be available for the construction. Thus, you can make it just like a 'compass and straightedge' construction, or you can allow the student to be able to make parallel lines, angle bisectors, or even centroids, simply by clicking on  the appropriate button. The constructions can be either simple or tricky, depending.
  2. Secondly, in proof mode, it allows the student to work his or her way through a proof. The program checks all the steps of a proof as the student performs them and gives immediate feedback as to whether the step is justifiable or not. (The entire concept of proof is probably the hardest one for most students!) Proof exercises specify which theorems, postulates, properties, and definitions are available for use by the student, but the student can work through the proof in any one of a very large number of different possible logical paths.
The program was written by Jacques Gressier of the Academy of Lille, and the original exercises were written in French (and designed for the French national curriculum) by Bernard Montuelle and  Danièle Fosseux.  (All 3 live and work in northern France, in the region near Boulogne-sur-Mer, a bit south of Calais). I (Guy Brandenburg)  heard about the program via one of the math-teacher list-serves on the Math Forum, and was intrigued. I eventually translated the program's interface into American English, adapted or wrote from scratch 200 construction and proof exercies, and wrote the 80-plus-page manual. It helped a lot when I went to France and met with the original authors (and enjoyed the wonderful French hospitality of the lovely Montuelle family!) to learn more about how it works - some things are much harder to communicate by e-mail than in person. (My French is not too bad - I went to school for two widely separated years as a youngster and earned a Baccalauréat in Mathématiques Elémentaires in 1967.) The American version of the program is published by Sunburst. The French version is published by CDE4. Here are links to Geometrix.    Jacques Gressier's Web Pages on Geometrix (in French and English)   and Sunburst catalog page on Geometrix  and CDE4 website (in French)
  • The following diagram is a classic of chaos theory.  It shows what happens (after about 100 iterations) when the output from the function a=k*b*(1-b) gets fed into itself, as k varies. As k gets larger, you start to get two different levels of output, then four different levels, then 8, then you get extremely strange, chaotic behavior. Writing the code to implement this chaotic diagram is actually very easy (you can do it on a graphing calculator), but I used Fractint to create this.

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click on the thumbnail sketch above to see a full-sized diagram  with more detail.  

A few more fractal images or links:

Astronomy clubs not too far away from Washington, DC: A few more astronomy resources:

Links to other math, science, geometry, and mathematics-education resources

Send comments, feedback and suggestions to me at
mailto:gfbrandenburg@yahoo.com

Last modified by Guy Brandenburg on October 25, 2003