# Public Domain Math

Many pieces of mathematics — for example, simple geometric shapes and some mathematical formulas — are uncopyrightable or unpatentable. You can’t copyright a square or patent the area formula for a circle. Anyone can use them. But this post is not about the intricacies of patent or copyright law as they apply to mathematics, as fascinating as that can be. This is about different public domain math.

An image from Max Brückner’s 1900 book Vielecke und Vielflache: Theorie und Geschichte (Polygons and Polyhedra: Theory and History). Credit: Public domain, via Internet Archive

The Public Domain Review is a website and nonprofit project that highlights weird and wonderful work that is in the public domain. (The definition of public domain varies by country; Public Domain Review labels their posts with further information if necessary.) I love seeing their posts in my blog feed because they are so varied and interesting. Some are beautiful, some are strange, some are funny. And some are math.

C. H. Hinton used multicolored cubes to illustrate the tesseract. Credit: Public domain, via Internet Archive

For instance, this article by Jon Crabb looks into some interesting late nineteenth and early twentieth century writings on dimension. Edwin A. Abbott’s Flatland: A Romance of Many Dimensions is fairly familiar to mathematicians. It’s some of the most effective math communication I’ve ever read, and as a bonus, you get vicious satire of Victorian social structures. I was unaware of C. H. Hinton’s 1904 treatise The Fourth Dimension, which runs away with the idea of a fourth spatial dimension. But it turns out I had already interacted with him, or at least a piece of his legacy: he coined the term tesseract for the four-dimensional analogue of the cube (also called a four-dimensional hypercube). Hinton believed the fourth dimension had psychic as well as physical implications, and his ideas about the fourth dimension influenced artists and writers including Marcel Duchamp and Gertrude Stein. Hinton’s book uses colored cubes to visualize the many cubes in a tesseract. Hinton was married to Mary Ellen Boole, one of the remarkable daughters of George and Mary Everest Boole.

Then there’s one of my favorite examples of design meeting mathematics: the 1847 Oliver Byrne edition of the first six books of Euclid’s Elements. And Ernst Chladni’s figures illustrating the nodes of vibrating plates. And Étienne Léopold Trouvelot’s astronomical illustrations, including a beautiful depiction of a total solar eclipse.

Credit: Public domain, via New York Public Library

Browsing through the mathematics tag, it’s fun to see work from people with enduring legacies as well as some things that are a little out thereMathematics shows up in some unexpected places. You can try to find frieze and wallpaper groups in an 1863 book of French textile samples or identify the curves in a 1919 book of Japanese wave and ripple designs. You can learn the correct proportions for Buddha and Bodhisattva depictions from an eighteenth-century book from Nepal. You can take a peek at early twentieth century data visualization in the infographics W. E. B. DuBois and his students created depicting various facets of African American life.

The Public Domain Review publishes a lot more than just math and science. It’s a worthy addition to the blogroll for all the interesting artifacts it brings to light, from math and science to art and religion.

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