Most authors of math texts do not design their books with two-page spreads in mind. Typically, an author types in LaTex, and trusts LaTex to handle all the formatting, page layout, etc.. But for an illustrated book, I care about page layout. I want the reader to open the book to any page, and find the content on the left complementary to the content on the right.

A few software innovations have made the illustration and layout of this book possible and free. One is the Tufte-LaTex package, which imitates the layout of Tufte’s books, especially the spacious margins for sidenotes. Another is the combination of PGF and TikZ for illustrations within LaTex. This package outputs to beautiful PDF, with color control in the CMYK colorspace. Moreover, using basic programming constructs within PGF/TikZ (and sometimes using personal Python scripts to output TikZ code), one can precisely place dots and weighted lines as necessary for mathematical figures, and integrate these figures seamlessly with text.

Below is a two-page spread (click to enlarge!) from the first chapter of the book, in which I count pairs in the set $\{1,2,3,4,5,6,7,8,9,10\}$.

The figure on the right-page exhibits what Tufte calls “small multiples”. There are 45 possible 2-element subsets of $\{1,2,3,4,5,6,7,8,9,10\}$. To illustrate the connection between 2-element subsets and points in a triangular arrangement, I produced a picture of all 45 subsets! Each small illustration (small triangle) fits into a large triangle, and the location of a small triangle in the large triangle also matches the location of a blue dot within the small triangle. The reader is meant to connect Figure 1.4 on the left page to the large figure on the right page, as the blue dots, red dots, and blue lines correspond (after a bit of rotation and folding).