The Magic Theorem

“The Magic Theorem is a joyful exploration of symmetry and the elegant geometry of orbifolds. Conway, Burgiel, and Goodman-Strauss have created something rare: a book that distills deep mathematics into a playful, visually stunning experience. Whether you're encountering these ideas for the first time or rediscovering them with fresh eyes, this is a guided tour filled with clarity, wonder, and charm.”

—Steven Strogatz, Professor of mathematics at Cornell University and bestselling author of Infinite Powers

"The present book has a predecessor: The Symmetries of Things, by the same authors, a hefty 400 pages, published in 2008. Conway still worked significantly on this new work, therefore, while his co-authors Heidi Burgiel and Chaim Goodman-Strauss have "much expanded and much abridged" it for this new version, meaning they omitted numerous consequences of the orbifold concept and instead expanded the introduction up to the magic theorem through a wealth of examples. The older book wanted to appeal to "laypeople, artists, active mathematicians, and researchers in general." This new work undoubtedly fulfils this claim as well.

As for me, the restriction of the new version to the first part of The Symmetries of Things was actually successful. While I never dared approach the old, much longer book, I was able to consume the new one with profit. And this despite the fact that I haven't been so keen on practice problems since the end of my studies and have skipped the abundantly scattered exercises ("Here is a pattern, find its symmetries")."

—Christoph Pöppe, Spektrum der Wissenschaft (translated from the original German article)

“The Magic Theorem is a joyful exploration of symmetry and the elegant geometry of orbifolds. Conway, Burgiel, and Goodman-Strauss have created something rare: a book that distills deep mathematics into a playful, visually stunning experience. Whether you're encountering these ideas for the first time or rediscovering them with fresh eyes, this is a guided tour filled with clarity, wonder, and charm.”

—Steven Strogatz, Professor of mathematics at Cornell University and bestselling author of Infinite Powers

"The present book has a predecessor: The Symmetries of Things, by the same authors, a hefty 400 pages, published in 2008. Conway still worked significantly on this new work, therefore, while his co-authors Heidi Burgiel and Chaim Goodman-Strauss have "much expanded and much abridged" it for this new version, meaning they omitted numerous consequences of the orbifold concept and instead expanded the introduction up to the magic theorem through a wealth of examples. The older book wanted to appeal to "laypeople, artists, active mathematicians, and researchers in general." This new work undoubtedly fulfils this claim as well.

As for me, the restriction of the new version to the first part of The Symmetries of Things was actually successful. While I never dared approach the old, much longer book, I was able to consume the new one with profit. And this despite the fact that I haven't been so keen on practice problems since the end of my studies and have skipped the abundantly scattered exercises ("Here is a pattern, find its symmetries")."

—Christoph Pöppe, Spektrum der Wissenschaft (translated from the original German article)