Beautiful Geometry

Eli Maor + Eugen Jost

Princeton University Press 2017

Math Art: Truth, Beauty, and Equations

Stephen Ornes

Sterling 2019

Bilder der Mathematik

Georg Glaeser + Konrad Polthier

Springer 2014
A book review by Danny Yee © 2020
Attempts to link mathematics and art are often rather tenuous, but Math Art and Beautiful Geometry both make some substantial connections, approaching from almost opposite directions.

In Beautiful Geometry, Maor has written fifty one brief (three or four page) pieces, mostly on single constructions or theorems taken from geometry, but with some ventures into number theory: "The Golden Ratio", "The Pentagon", "Fifty", "Lissajous Figures", and so forth. Jost has then created art to illustrate those, in the form of one or two full-page colour plates for each piece. Sometimes these are more tangential, but mostly they directly illustrate the ideas in the text, only more attractively and creatively than traditional diagrams (some of which are also used).

In Math Art, in contrast, Ornes starts each of his nineteen chapters with a biography of an artist whose work has been inspired by or used mathematics — many of them are mathematicians themselves — illustrated with photographs of their work. This is then followed by a separate "math behind the art", introducing a broad area of mathematics as well as considering its use in specific works. "Space and Beyond", for example, looks at the life and work of Bathsheba Grossman, with pictures of her work including a full page photograph of her Gyroid sculpture; the accompanying "math behind the art" introduces minimal surfaces and describes Alan Schoen's 1968 discovery of the gyroid.

Beautiful Geometry is historical and biographical in approach, with most of the material covered coming from classical and early modern geometry, and proceeds roughly chronologically. In Math Art, in contrast, Ornes covers contemporary artists rather than more famous ones, and much of the mathematics touched on is more modern — fractals, the travelling salesman problem and the P-NP distinction, quantum computing, and so forth.

Math Art assumes almost no background knowledge. Beautiful Geometry assumes elementary high school geometry and algebra, and doesn't shy from equations, but the few actual proofs are pushed to an appendix. Because both works consist of entirely independent short chapters, they should be very broad accessible. Both should be in school libraries.

Bilder der Mathematik (currently only available in German but due to be published in 2021 as A Mathematical Picture Book) has a similar structure to Beautiful Geometry, with over 150 one or two page explanations of mathematical ideas that tightly combine text and illustration. Glaeser and Polthier eschew any mention of art (Kunst), preferring instead the term visualisation (Visualisierung), but their illustrations are attractive as well as functional and the distinction seems moot.

Focused entirely on the mathematics, with little or no "popular" digressions to biography or history, Bilder der Mathematik packs in quite a bit, including much that was new to me. It is pitched perhaps at undergraduates, less because it requires much actual mathematics than because it assumes a general familiarity with the language and conventions of the discipline. But the pieces are entirely independent and can be read in any order, starting anywhere, and should be quite broadly accessible.

June 2020

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Related reviews:
- Lynn Gamwell - Mathematics and Art: A Cultural History
- Eli Maor - Music by the Numbers: From Pythagoras to Schoenberg
- books about art + art history
- more biography
- books about mathematics
- books about popular mathematics
- books published by Princeton University Press
- books published by Springer
%T Beautiful Geometry
%A Maor, Eli
%A Jost, Eugen
%I Princeton University Press
%D 2017
%O paperback, bibliography, index
%G ISBN-13 9780691175881
%P 187pp

%T Math Art: Truth, Beauty, and Equations
%A Ornes, Stephen
%I Sterling
%D 2019
%O hardcover, illustrations, bibliography, index
%G ISBN-13 9781454930440
%P 192pp

%T Bilder der Mathematik
%A Glaeser, Georg
%A Polthier, Konrad
%I Springer
%D 2014
%O paperback, illustrations
%G ISBN-13 9783662434161
%P 340pp