From my old webpage:

Areal photo of Dupont Circle in Washington, DC reveals an (approximate) rare 10-fold symmetry. There are many circles in Washington (according to Wikkipedia there are 33), but  no  other has the full 10-fold symmetry of Dupont circle.

Penrose tilings, discovered circa 1976 by Roger Penrose. This most highly "symmetric" Penrose tiling is called the "Cartwheel" by John H. Conway.

The basic plan for the city, including the layout of Dupont Circle, is due to Pierre l’Enfant (small insert), circa 1791. Notice the diagonal "state" streets.

Penrose tiling decorated with the Ammann bars, discovered by amateur mathematician Robert Ammann  (http://tilings.math.uni-bielefeld.de/people/r_ammann). Note how much the bars resemble "state" streets in Washington. This image can be made to more closely resemble the city plan if it is skewed to make two of the directions perpendicular.

Place Charles de Gaulle in Paris with 12-fold symmetry(!), but with no underlying grid.

Penrose tiling mural at GWU Department of Mathematics



There is, of course, a long history of second guessing the motives of those who designed the city of Washington. See for example this, this, or this. Is there a conspiracy here? See this.

This post contains materials from lectures I have periodically given to students about setting up and using LaTeX. It also describes several other software packages that students may want to learn to use and install on their computers.

Distributions (what to install):

A version of LaTeX can be installed for free on your computer no matter what kind of computer/OS you have:

  1. MikTeX (for Windows): http://miktex.org
  2. MacTeX (for Mac): http://www.tug.org/mactex/
  3. TeXLive (for Linux, BSD, etc.): install the version of LaTeX available through your package manager.



The "Three M's" of commercial Mathematics software. Mathematica and Maple are "Computer Algebra Systems" (CAS) with an emphasis on symbolic computing, while Matlab is a numerical computing based system. GW has a site license for Mathematica which allows all GW students free installs (see here). Maple and Matlab are available in campus computer labs. All of the above (and most below) have excellent graphical capabilities.

There are various free alternative software packages that can replace the rather expensive software dicaussed above: Instead of Mathamatica or Maple, consider using wxMaxima (GUI for open source version of Maxima, one of the earliest CAS. Not as fully featured as its commercial cousins, but decent). Or try the huge Sage (based on Maxima, Python and many other packages). Two decent free Matlab alternatives are GNU Octave or Scilab.

For any work involving statistics or data you would do well to consider R. It can also do a lot of what Matlab can do.

Also, Python together with some of its packages (NumPy, SciPy, Mathplotlib, SymPy) can do a lot of what all of the above can do.  Sage (see above) contains a full implementation of Python with all of the mentioned packages installed, but you might also consider a distribution like Anaconda, which is just Python together with a selection of packages for technical computing.

Sample LaTeX Documents:

Classroom examples (from Math 2572):

Basic document: README.docx, basic.tex
Less basic: README.docx, Class2Lecture.tex, Class2Lecture1.pdf
Even less basic: Class3Lecture.tex, Class3Lecture1.pdf, picture1.pdf


Homework: homework.tex, homework.pd
Dissertation: dissertation.te

Real Examples:

Research Paper 1: paper1.tex, paper1.pdf, journal1.pdf
Research Paper 2: paper2.tex, paper2.pdf, Rot.pdf,
Slide Show: BeamerTemplate.tex, KIAS.pdf, KAIS.zip

Comment: For each item above, download all the associated files into the same directory (so that LaTeX can find them). Then open the .tex file (in TeXWorks or the like) and run LaTeX (pdfLaTeX version). In some cases a sample .pdf output or README is also included.


Drawing and graphics: Inkscape. Gimp. Irfanview (Windows only, unfortunately).
Postscript and PDF: Ghostscript/Ghostview
GUI Interface for LaTeX: LyX