# Dissection Font

## by Erik Demaine, Martin Demaine, Donald E. Knuth, Yushi Uno, 2018

 Enter text to render:   text Letter without dissection Dissection in form of letter Dissection in form of square Dissection in both forms Grid 4-piece disconnected font 2-piece disconnected font 3-piece connected font 2-piece connected font

In these fonts, each letter or digit or ampersand can be dissected (cut into pieces such that those pieces re-arrange) into a 6 × 6 square. The dissections all happen to be polyomino dissections, and they allow translation, rotation, and reflection in the piece re-arrangement. There are four different fonts, each using up to 2, 3, or 4 pieces in each dissection. Of course, with more pieces, it is easier to get nicer-looking letters. The 2- and 4-piece disconnected fonts use some disconnected pieces (but still each piece moves as a single unit), while the 2- and 3-piece connected fonts use connected pieces. In the disconnected fonts, we achieve uniform letter heights.

Origin. The 3- and 4-piece font come from a draft of The Art of Computer Programming, volume 4, pre-fascicle 9B “A Potpourri of Puzzles”, where Knuth poses (and solves) two exercises in mathematical/puzzle font design. See Knuth's December 2018 profile in the New York Times. These fonts were originally presented at Knuth's 80th Birthday Party in January 2018. The 2-piece disconnected font was released in May 2019.

Font forms. Each font can be presented in a fully solved form (“Dissection in both forms”) or in a variety of puzzle forms. “Letter without dissection” is the hardest form: the puzzle for each letter is to find a dissection with the specified number of pieces into a 6 × 6 square. In “Dissection in form of letter”, the puzzle is to find the re-arrangement of the letter into the square (a relatively easy puzzle). In “Dissection in form of square”, the puzzle is to figure out which letter the pieces can re-arrange into; this form is a puzzle font in the sense that reading the message requires solving the puzzle.

Related mathematics. It has been known since 1814 that every two polygons of the same area have a dissection (and even a hinged dissection), but finding a dissection with the fewest possible pieces (or a specified number k of pieces) is strongly NP-complete.

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