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Among the uppercase letters, "S" is the only one that's not either based on a single primary ellipse, or combined with straight lines that provide structural constraints. The entire glyph is governed by continuously changing curvature with no stabilizing axis or primitive shape to enforce proportions.

This results in a more complex and less obvious mathematical definition.

Also, a naively symmetrical "S" tends not to look good, probably because of these same issues, so needs further adjustment to match our visual expectations. This complicates the definition further.

by noufalibrahim11 hours ago|

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If you do lettering by hand, S has a bit of reputation. It's hard to get right. Small mistakes stand out even to an untrained eye. However, once you do get it (subjectively) right, it's an extremely beautiful letter. This is even more true in hands like cancellaresca corsiva (the so called "italic font") where the letters are somewhat smooth flowing rather than built with rigid lines. More interestingly, because of all these parameters, you can play a lot with the letter especially if you want to do it as a drop cap or ornament it. As an example, making the lower bowl bigger as the the above comment invites gives the letter some personality.

This is all fine. What fascinates me with Knuth's work is how he applies mathematical rigour to concepts like these which are generally considered "artistic" and subjective. It underlines how mathematical ideas of symmetry etc. play a role in making the world we live in beautiful.

by whatshisface9 hours ago|

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As Knuth points out, applying math to art is applying artistic sense to a continuum of forms all at once.

by noufalibrahim7 hours ago|

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That's a nice quote.

I remember seeing an animated documentary as a child called "Donald in Mathmagic Land" which ends with a quote attributed to Galileo.

> Mathematics is the language with which God has written the universe

by jll299 hours ago|

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