# Mathematical and Puzzle Fonts/Typefaces

## Erik Demaine, Martin Demaine, and others

Scientists use fonts every day to express their research through the written word. But what if the font itself communicated (the spirit of) the research? What if the way text is written, and not just the text itself, engages the reader in the science?

Below are mathematical typefaces we designed through inspiration which are inspired by mathematical theorems or open problems. Most include a puzzle font: reading them is itself a mathematical puzzle.

All fonts are available to play with as web applications which run entirely in your (modern) browser, including iOS and Android.

For more information, read our paper “Fun with Fonts: Algorithmic Typography” and other papers listed below, or check out media coverage in The New York Times, Science News (text available here), and Gizmodo.

Integer sequence font by Éric Angelini, Erik Demaine, Martin Demaine, and Carole Dubois, 2023
• Letters, words, or text plotted by a finite sequence of integers.
• Self-plotting infinite integer sequence rejected by the OEIS.
Orthogonal fold & cut font by Joshua Ani, Josh Brunner, Erik Demaine, Martin Demaine, Dylan Hendrickson, Victor Luo, and Rachana Madhukara, 2022.
• Each letter is made from a square of paper by a sequence of orthogonal folds followed by one straight cut.
Yin-Yang font by Erik Demaine and Martin Demaine, 2021.
• Each letter is an interactive Yin-Yang puzzle whose unique solution forms the image of the letter.
Sudoku font by Erik Demaine and Martin Demaine, 2021.
• Solve each Sudoku puzzle; then the longest path through consecutive adjacent numbers (differing by exactly 1 in edge-adjacent squares) draws each letter.
Everything font by Erik Demaine and Martin Demaine, 2021.
• Every letter-shaped piece of paper can be folded into every other letter (slightly smaller), via an intermediate "E" shape.
Tiling font by Erik Demaine, Martin Demaine, Scott Kim, and Yushi Uno, 2021.
• Each letter tiles the infinite plane without gaps.
Path Puzzles font by Jeffrey Bosboom, Erik Demaine, Martin Demaine, Adam Hesterberg, Roderick Kimball, and Justin Kopinsky, 2020.
• Each letter is an interactive path puzzle whose unique solution forms the path of the letter.
Tatamibari font by Aviv Adler, Jeffrey Bosboom, Erik Demaine, and Martin Demaine, Quanquan Liu, and Jayson Lynch, 2020.
• Each letter is an interactive Tatamibari puzzle whose unique solution forms the image of the letter.
Tetris font by Erik Demaine and Martin Demaine, 2020.
• Each letter is built by dropping exactly one of each of the seven Tetris (tetromino) pieces in some sequence.
Cube folding font by Oswin Aichholzer, Hugo Akitaya, Kenneth Cheung, Erik Demaine, Martin Demaine, Sándor Fekete, Linda Kleist, Irina Kostitsyna, Maarten Löffler, Zuzana Masárová, Klara Mundilova, and Christiane Schmidt, 2019.
• Each letter is a puzzle: can you fold it into a 1 × 1 × 1 cube?
Impossible folding font by Erik Demaine, Martin Demaine, Tomoko Taniguchi, and Ryuhei Uehara, 2019.
• Each letter is an impossible object called a hypercard: it can be cut and folded from a single square of paper, even though the vertical flap cannot be flattened into the horizontal plane without material overlapping.
Dissection font by Erik Demaine, Martin Demaine, Donald E. Knuth, and Yushi Uno, 2018.
• Each letter can be dissected into a 6 × 6 square.
• Three different fonts uses exactly 2, 3, or 4 pieces in each dissection.
• Each letter is made up of two simple symbols: a U shape and a line. Both symbols are in every letter, and every U shape has exactly the same proportions; the shapes are just rotated and/or scaled.
• Puzzle and animation fonts can be made by rotating the basic symbols.
Checkers font by Jeffrey Bosboom, Spencer Congero, Erik Demaine, and Martin Demaine, and Jayson Lynch, 2018.
• Each letter is an 8 × 8 cooperative always-jumping checkers puzzle. The solution sequence can be animated!
• Such puzzles are NP-complete in general, as proved in our paper “Losing at Checkers is Hard”.
Spiral Galaxies font by Walker Anderson, Erik Demaine, and Martin Demaine, 2018.
• Each letter is a Spiral Galaxies puzzle whose unique solution forms the image of the letter.
• You can interactively solve the puzzles.
• Each letter is formed by folding two translucent symbols on top of each other, as in silhouette puzzles.
Coin sliding font by Erik Demaine and Martin Demaine, 2018.
String art font by Erik Demaine, Martin Demaine, and Petros Vrellis, 2017.
• In one font (shown), each letter is a thread wrapped 1,500 times around 200 pins.
• In other fonts, each letter is a thread wrapped around just 22 pins, and involves puzzles related to Euler tours.
Strip folding font by Erik Demaine and Martin Demaine, 2017.
• An entire sequence of letters folds from a single strip of paper.
Voronoi font by Erik Demaine and Martin Demaine, 2017.
• Each letter is the Voronoi diagram of a set of points.
Fold and punch font by Erik Demaine and Martin Demaine, 2017.
• Each letter from a square of paper by a sequence of simple folds followed by one circular hole-punch.
• Each letter is made from a square of paper by a sequence of simple folds followed by one straight cut.
Tangle font by Erik Demaine, Martin Demaine, and Ronald Taylor, 2016.
• Each letter is a flat configuration of a Tangle of identical length, presented graphically or as a NSEW sequence.
Juggling font by Erik Demaine and Martin Demaine, 2015.
• Each letter is a juggling pattern, animated by the Juggling Lab software or summarized by a single image of the ball trajectories.
Card shuffling font by Erik Demaine and Martin Demaine, 2015.
• By a sequence of perfect shuffles of 26 cards labeled A through Z, the magician can present the letters of your message in order.
Glass cane font by Erik Demaine and Martin Demaine, 2014.
• Each letter is a glass cane, a cylinder of glass made by pulling and twisting an arrangement of straight lines of colored glass embedded within clear glass, as simulated by our Virtual Glass software.
Linkage font by Erik Demaine and Martin Demaine, 2014.
• Each letter/number is a fixed-angle linkage (which model protein folding) designed so that random configurations can be uniquely decoded back to text.
• Hot glass components are arranged (in the puzzle font) so that squishing them horizontally produces a letter (in the clear font)
• Video font illustrates physical squishing to form the letters
Origami maze font by Erik Demaine, Martin Demaine, and Jason Ku, 2010.
• The font can be folded as extruded letters from a rectangle of paper, using an algorithm for folding orthogonal graphs by the same authors.
Conveyer belt font by Erik Demaine, Martin Demaine, and Belén Palop, 2008.
• The form without the belts (lines) is a puzzle to decode, based on a mathematical open problem by Manuel Abellanas first posed in 2001.
Hinged dissection font by Erik Demaine and Martin Demaine, 2003.
• One hinged chain of (128) pieces folds into any of the letters in the alphabet as well as a square.

## Other Related Fonts

Here are some other fonts in the same genre as the mathematical/puzzle fonts above, but by other people.

Peg solitaire font by Taishi Oikawa, Kazuaki Yamazaki, Tomoko Taniguchi, and Ryuhei Uehara, BRIDGES 2017.
• Each letter is a reachable pattern in the game of Peg Solitaire from an initially full 5 × 7 board.
• The puzzle is to figure out how to reach each such pattern!
3 × 5 origami font by Yoshihisa Matsukawa and Jun Mitani, 2016.
• Each letter is the silhouette of a flat origami folded from a 3 × 5 box-pleated grid.
• Based on an enumeration of all such silhouettes by Matsukuwa, Yamamoto, and Mitani, which appears at ICGG 2016.

## Papers

Here are papers we have written about mathematical/puzzle fonts/typefaces, including both surveys and research papers that include fonts:

Last updated May 22, 2023 by Erik Demaine.Accessibility