Mathematical graphics

Admiring graphics is an old idea:

Manuscripts should be decorated so that their appearance alone will induce perusal ...
beware that this art work does not become an end in itself.
From In praise of scribes by Johannes Trithemius, c. 1492
(translation by Roland Behrendt)

Not everybody thinks pictures are an improvement:

Discourse was deemed Man's noblest attribute,
and written words the glory of his hand;
Then followed printing with enlarged command
For thought---dominion vast and absolute
For spreading truth, and making love expand.
Now Prose and verse sunk into disrepute
Must lacquey a dumb Art that best can suit
The taste of this once intellectual Land.

A backward movement surely have we here,
From manhood---back to childhood; for the age---
Back towards caverned life's first rude career.
Avaunt this vile abuse of pictured page!
Must eyes be all in all, the tongue and ear
Nothing? Heaven keep us from a lower stage.

Wordsworth, as quoted on p. 7 of Fallodon Papers by Viscount Grey of Fallodon

... this technologically driven evolution away from `logocentrism' often associated with modernity
and progress ... projects us into dangerously archaic states of collective consciousness.

Yuri Manin in The notion of dimension in geometry and algebra

Anyway, almost everybody likes pictures:

Each picture told a story; mysterious often to my undeveloped understanding ... yet ever profoundly interesting.

From the opening chapter of Jane Eyre

And almost everybody has advice to offer: The commentary must not repeat what the pictures already convey
but should enlarge and enhance the pictures.
... pictures could speak, without words, and convey ...
`highly complicated, abstract notions with economy, precision, and style.'

From the chapter `Hellas revisited' of Greece in my life by Compton Mackenzie, 1960 We intend to provide here a collection of tools for producing graphics in mathematical exposition, both in papers and on the Internet.

A PostScript manual for mathematicians.

This is a text for a course at UBC on Euclidean Geometry! The theme of the course is how to use computers to produce clear demonstrations in mathematics, but along the way it provides a complete introduction to PostScript.

Putting labels in PostScript figures.

When asked what irks them most about trying to include good illustrations in mathematical papers, most mathematicians complain about the difficulty of adding mathematical labels. This is one solution, although admittedly somewhat intricate.

Dealing with colour.

Colours on computer screens, and p[articularly inside a browser, are not perfect. This gives you some idea of what to expect.

DVIPS.

The manual for dvips in .pdf format.

Byrne's Euclid.

A beautiful if eccentric example of how to explain mathematical ideas with illustrations.

A review of Edward Tufte's book Visual Explanations (from the American Mathematical Society Notices of January 1999).

Tufte's books are aimed at a general audience, but have something to offer to mathematicians. Including an example of how to use illustrations to make a mathematical argument.

Java image applets.

To publish mathematics on the Internet, a variety of figure manipulations is necessary. Here is the beginning of a collection of tools for doing that.

A PostScript drawing toy.

This will some day expand to a general tool for working interactively to produce PostScript figures.

An interactive PostScript interpreter.

Scott Drader has written a PostScript interpreter in Java, using the Java 5.0 2D library, that allows interaction as programs are being run. This includes being able to step through a PostScript program, setting breaks and variable watches. The present version is still a bit slow and buggy, but worth looking into. Problems should by all means be reported to cass@math.ubc.ca.