The Letter S, by Donald Knuth (1980) [pdf]

bombcar

I just spent 30 minutes reading a detailed mathematical version of "draw an S; next draw a more different S".

WillAdams

His book _TeX and METAFONT_ (about the initial public release) goes into these difficulties in greater detail and includes the charming response by his wife when shown some initial efforts: >Why don't you make them _S_ shaped? To some degree, this problem was eventually solved, c.f., the five volume set _Computers and Typesetting_: https://www-cs-faculty.stanford.edu/~knuth/abcde.html but then one had the effort to create a new typeface set for math equations by the AMS, eventually named Euler as written up in "AMS Euler — a new typeface for mathematics". _Scholarly Publishing_ and so forth, but arguably, things went awry in that rather than capture the ductus of Prof. Zapf's pen, and model based on that stroke and a pen shape, the expedient approach of simply modeling the outline was arrived at and implemented due to the difficulty and lengthy time required for the idealized approach. Another consideration may have been that there doesn't seem to be an available algorithm which is robust and accurate and automatic for determining the curves which describe the union of arbitrary Bézier curves (some projects get around this by making high resolution pixel images and tracing them).

mrandish

Knuth is just a treasure.

adm4

Wonderful man, here is a lecture on the topic from Joint Mathematics Meeting, Étienne Ghys. https://www.youtube.com/watch?v=1OIxzewWilc

fraserphysics

This article was in Springer's The Mathematical Intelligencer in 1980. The next article in that volume was "Strange Attractors" by David Ruelle. When I read Ruelle's article in the early 1980s, I noticed Knuth's article. By the time I got to writing my third paper on strange attractors in 1988, I was using TeX.

bananaflag

It's not clear to me why the S is more difficult than the others.

tobr

I was just reading about Metafont the other day, so this was quite lovely to come across. Fig 9 stood out to me as obviously wrong. The two glyphs on the left are pixel by pixel identical, as are the three middle ones, and the two on the right. Quite mysterious though considering this PDF appears to be a scan.