# Mathematical and Puzzle Fonts/Typefaces

*by*Phil Tadros

Scientists use fonts every single day to specific their analysis by the written

phrase. However what if the font itself communicated (the spirit of) the analysis?

What if the best way textual content is written, and never simply the textual content itself, engages the

reader within the science?

Beneath are **mathematical typefaces** we designed by inspiration

that are impressed by mathematical theorems or open issues.

Most embrace a **puzzle font**: studying them

is itself a mathematical puzzle.

All fonts can be found to play with as net functions

which run fully in your (trendy) browser, together with iOS and Android.

For extra info, learn our paper “**Fun with Fonts: Algorithmic Typography**”

and different papers listed below,

or try media protection in

**The New York Times**,

Science News (text available here),

and

Gizmodo.

- Letters, phrases, or textual content plotted by a finite sequence of integers.
- Self-plotting infinite integer sequence rejected by the OEIS.

- Every letter is constituted of a sq. of paper by a sequence of orthogonal folds adopted by one straight reduce.

- Every letter is an interactive Yin-Yang puzzle

whose distinctive answer types the picture of the letter.

- Remedy every Sudoku puzzle; then the longest path by consecutive

adjoining numbers (differing by precisely 1 in edge-adjacent squares)

attracts every letter.

- Each letter-shaped piece of paper could be folded into each different letter

(barely smaller), through an intermediate "E" form.

- Every letter tiles the infinite airplane with out gaps.

- Every letter is an interactive path puzzle

whose distinctive answer types the trail of the letter.

- Every letter is an interactive Tatamibari puzzle

whose distinctive answer types the picture of the letter.

- Every letter is constructed by dropping precisely one among every of the seven

Tetris (tetromino) items 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.

- Every letter is a puzzle: are you able to fold it right into a

1 × 1 × 1 dice?

- Every letter is an inconceivable object referred to as a hypercard:

it may be reduce and folded from a single sq. of paper,

regardless that the vertical flap can't be flattened into the horizontal

airplane with out materials overlapping.

- Every letter could be dissected right into a 6 × 6 sq..
- Three totally different fonts makes use of precisely 2, 3, or 4 items in every dissection.

- Every letter is made up of two easy symbols: a U form and a line.

Each symbols are in each letter, and each U form has precisely

the identical proportions; the shapes are simply rotated and/or scaled. - Puzzle and animation fonts could be made by rotating the fundamental symbols.

- Every letter is an 8 × 8 cooperative always-jumping checkers puzzle.

The answer sequence could be animated! - Such puzzles are NP-complete on the whole, as proved in our paper

“Losing at Checkers is Hard”.

- Every letter is a Spiral Galaxies puzzle whose distinctive answer types the

picture of the letter. - You may interactively clear up the puzzles.

- Every letter is shaped by folding two translucent symbols on prime of one another, as in silhouette puzzles.

- In a single font (proven), every letter is a thread wrapped 1,500 instances

round 200 pins. - In different fonts, every letter is a thread wrapped round simply 22 pins,

and includes puzzles associated to Euler excursions.

- A whole sequence of letters folds from a single strip of paper.

- Every letter is the Voronoi diagram of a set of factors.

- Every letter from a sq. of paper by a sequence of easy folds adopted by one round hole-punch.

- Every letter is constituted of a sq. of paper by a sequence of easy folds adopted by one straight reduce.

- Every letter is a flat configuration of a Tangle of equivalent size, introduced graphically or as a NSEW sequence.

- Every letter is a juggling sample, animated by the

Juggling Lab software program

or summarized by a single picture of the ball trajectories.

- By a sequence of excellent shuffles of 26 playing cards labeled A by Z,

the magician can current the letters of your message so as.

- Every letter is a
**glass cane**, a cylinder of glass made by pulling and

twisting an association of straight traces of coloured glass embedded

inside clear glass, as simulated by our

Virtual Glass software program.

- Every letter/quantity is a fixed-angle linkage (which mannequin protein folding)

designed in order that random configurations could be uniquely decoded again to textual content.

- Sizzling glass parts are organized (within the puzzle font)

in order that squishing them horizontally produces a letter (within the clear font) - Video font illustrates bodily squishing to type the letters

- The font can be folded as extruded letters from a rectangle of paper,

using an algorithm for folding orthogonal graphs by the same authors.

- The shape with out the belts (traces) is a puzzle to decode, based mostly on a

mathematical open drawback by Manuel Abellanas first posed in 2001.

- One hinged chain of (128) items folds into any of the letters

within the alphabet in addition to a sq..

## Different Associated Fonts2>

Listed below are another fonts in the identical style because the mathematical/puzzle

fonts above, however by different folks.

**Peg solitaire font**by Taishi Oikawa, Kazuaki Yamazaki, Tomoko Taniguchi, and Ryuhei Uehara, BRIDGES 2017.

- Every letter is a reachable sample within the recreation of Peg Solitaire from an initially full 5 × 7 board.
- The puzzle is to determine the right way to attain every such sample!

- Every letter is the silhouette of a flat origami folded from a 3 × 5 box-pleated grid.
- Based mostly on an enumeration of all such silhouettes by Matsukuwa, Yamamoto, and Mitani, which seems at ICGG 2016.

## Papers2>

Listed below are papers we've written about mathematical/puzzle fonts/typefaces,

together with each surveys and analysis papers that embrace fonts:

- “Orthogonal Fold & Cut”, arXiv:2202.01293, 2022.
- “Universal Hinge Patterns for Folding Strips Efficiently into Any Grid Polyhedron”,
*Computational Geometry: Idea and Functions*, 89:101633, 2020. - “Impossible Folding Font”, in
*Proceedings of twenty second Annual Convention of BRIDGES: Arithmetic, Music, Artwork, Structure, Tradition (BRIDGES 2019)*, 2019. - “2,664 Coin-Sliding Font Puzzles”,
*Alternate Guide of the thirteenth Gathering for Gardner*, April 2018. - “Spiral Galaxies Font”,
*MOVES 2017: The Arithmetic of Varied Entertaining Topics*, quantity 3. - “Losing at Checkers is Hard”,
*MOVES 2017: Arithmetic of Varied Entertaining Topics*, quantity 3. - “Folding and Punching Paper”,
*Journal of Info Processing*, 25:590–600, 2017. - “Juggling and Card Shuffling Meet Mathematical Fonts”,
*Connections in Discrete Arithmetic: In Honor of Ron Graham's eightieth Birthday*, 2018. - “Fun with Fonts: Algorithmic Typography”,
*Theoretical Pc Science*, 586:111–119, 2015. - “Tangled Tangles”,
*MOVES 2015: Arithmetic of Varied Entertaining Topics*, quantity 2. - “Linkage Font”, in
*Alternate Guide of the eleventh Gathering for Gardner (G4G11)*, March 2014. - “Origami Maze Puzzle Font”, in
*Alternate Guide of the ninth Gathering for Gardner (G4G9)*, 2010. - “Conveyer Belt Alphabet Font”, in
*Alternate Guide of the ninth Gathering for Gardner (G4G9)*, 2010. - “Conveyer-Belt Alphabet”,

in*Findings on Elasticity*, 2010. - “Hinged Dissection of the Alphabet”,
*Journal of Leisure Arithmetic*, 31(3):204–207, 2003.