Put on your 3D glasses!
A unique treat of spatial geometry from 1959. Not just for math-lovers.
Last time, we merely got a taste of “graphic mathematics” by one the classics of function curves and reliefs in 3D: the German reference book Tables of Functions with Formulae and Curves by Eugen Jahnke and Fritz Emde, originally published in 1909.
This time we’re taking it to the next level and picking up a book on 3D anaglyph descriptive/solid geometry that actually requires 3D glasses to view: the Hungarian mathematician Imre Pál’s book Térláttatós ábrázoló mértan published in 1959. The book was translated to English in 1962 under the title Descriptive Geometry with Three-Dimensional Figures. It had German, Spanish, Russian and Slovak translations too.
Many years ago, I bought it just out of curiosity—it looked interesting, and I’d never seen anything like it before. Over the years, however, I’ve come to appreciate it more and more. And I finally got around to scanning it.
The book is essentially a handbook. On the one hand, it explains how to draw and construct these anaglyphic spatial figures; on the other hand, it demonstrates their applications in mathematics, physics, engineering, architecture, and again, cartography.
The book is structured according to the principle of progressing from simple to complex, beginning with straight lines and simple bodies, moving on to curves and spherical shapes and bodies, and concluding with irregular shapes and bodies and topographic and 3D relief visualizations.
It’s strange, because these abstract anaglyph images are interesting on their own. But their “holographic” effect really comes through when viewed with 3D glasses. If you don’t have any on hand, don’t worry! For example, the NASA’s website has instructions on how to make your own. In our case, I recommend buying cyan and red-coloured acetate at an art supply or stationery store, rather than blue and red.
When I posted a few photos of this book on Twitter a couple of years ago, the creative coding community immediately responded. Tony Chou rendered an anaglyph cube on Observable, and another user created anaglyphs in Processing.
I’m not sure how many possibilities there are in this in data visualization. In any case, there have been previous attempts; the statistician Jürgen Symanzik, in particular, has been working on this since the early 1990s.
I’d be also curious to see, for example, a storytelling project created specifically using this technique. Or even a map. If you know of any, please let me know!
