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## Mathematicians Devise Typefaces Based On Problems of Computational Geometry60

KentuckyFC writes: "Typeface design is something of an art. For many centuries, this art has been constrained by the materials available to typographers, mainly lead and wood. More recently, typographers have been freed from this constraint with the advent of digital typesetting and the number of typefaces has mushroomed. Verdana, for example, is designed specifically for computer screens. Now a father and son team of mathematicians have devised a number of typefaces based on problems they have studied in computational geometry. For example, one typeface is inspired by the folds and valleys generated by computational origami designs. Another is based on the open problem of 'whether every disjoint set of unit disks (gears or wheels) in the plane can be visited by a single taut non-self-intersecting conveyor belt.' Interestingly, several of the new typefaces also serve as puzzles in which messages are the solutions."
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## Mathematicians Devise Typefaces Based On Problems of Computational Geometry

• #### I think i will stick with Times New Roman... (Score:1)

...before having to decipher those dots and lines
• #### Re: (Score:3)

You didn't actually see the font, the first image was just about analyzing character structure in a mathematically objective way.

• #### Re: (Score:1)

by Anonymous Coward

There is no "the font", the paper contains a number of fonts, one of which was the first image in the article. RTFA before telling people to RTFA, sheesh!

• #### Re: (Score:2)

I didn't. RTFP.

• #### Question answered (Score:5, Insightful)

on Friday April 18, 2014 @08:41AM (#46786977)

Well, at least now we know why typefaces are designed by artists and not mathematicians.

• #### Re:Question answered (Score:4, Insightful)

on Friday April 18, 2014 @08:48AM (#46787011)
I don't know, Computer Modern didn't turn out all that wrong.
• #### Re:Question answered (Score:5, Insightful)

on Friday April 18, 2014 @08:56AM (#46787053)

True, but I would say that was created by Knuth in the role of artist, not mathematician.

• #### At least ... (Score:3, Funny)

by Anonymous Coward

Well, at least now we know why typefaces are designed by artists and not mathematicians.

Next thing you know we're going to have software engineers designing user interfaces and wording menus ... oh wait.

• #### missing the point? (Score:5, Insightful)

on Friday April 18, 2014 @08:45AM (#46786997) Homepage

Traditionally, typeface designers have considered legibility and aesthetics in their work (in addition to typesetting limitations). Apparently those factors are optional now as well.

OK, these are interesting intellectual exercises. But don't try to sell them as examples of typeface design, because that's a creative discipline that goes beyond mathematical questions of "can it be done?"

• #### Re:missing the point? (Score:4, Insightful)

on Friday April 18, 2014 @08:53AM (#46787039) Homepage Journal

Yes, every characteristic is optional. e.g. comic sans and windings. Attempting an objective solution to an artistic problem isn't bad, the complaints that come out of that can help point you towards better objective constraints. Assuming you've succeeded because you're trying to be objective would be the only problem.

• #### Re:missing the point? (Score:4, Funny)

by Anonymous Coward on Friday April 18, 2014 @08:54AM (#46787047)

Traditionally, typeface designers have considered legibility and aesthetics in their work (in addition to typesetting limitations). Apparently those factors are optional now as well.

Since context, meaning, grammar, and style all seem to be actively discouraged in modern communication, why not use an illegible font as well?

• #### Re: (Score:3, Informative)

The funny thing is that this sort of mathematical and reductionist take on font "design" is precisely what modernism and then postmodernism did to other art forms — by stripping a tradition of its presupposed axioms, picking a certain point as a "first principle", establishing an alternative deriviation from it, and then calling that "art". I hope the typographers hold out, unlike what has become of fields such as sociology, post-tonal music, and continental philosophy.
• #### Re: (Score:2)

The funny thing is that this sort of mathematical and reductionist take on font "design" is precisely what modernism and then postmodernism did to other art forms â" by stripping a tradition of its presupposed axioms, picking a certain point as a "first principle", establishing an alternative deriviation from it, and then calling that "art".

Umm, I don't think you know what postmodernism [wikipedia.org] is. You're actually describing something closer to "modernism" in most art forms, which was generally about rejecting traditional aesthetic criteria and founding new systems. Postmodernism, as a broad artistic idea, is largely a reaction against these "modernist" systems, often drawing on older, more traditional techniques and styles, perhaps in novel or eclectic ways.

For example, you include "post-tonal music" as your only representative art form, but many

• #### Interesting... but nearly useless (Score:4, Insightful)

on Friday April 18, 2014 @08:48AM (#46787013)
The major point of fonts is to improve communications. Clarity and lack of ambiguity are pretty much the main goals we are striving for, with style being important but not vital. These two decided to have some fun with what could be done, and they succeeded. Good for them. Unfortunately, in achieving the style, they failed on the clarity. Time to turn the page.
• #### Re: (Score:3, Interesting)

by Anonymous Coward

You misunderstand the point of the exercise entirely. None of these fonts are intended for use. Rather, the alphabet provides a useful set of 26 shapes upon which these geometric techniques / problems can be modeled. The alphabet is being used as a set of "testing data," nothing more, and provides an interesting and relatable look at various problems in geometry.
However, the fact that this testing data can also be used for communications makes already-interesting demonstration of areas of inquiries in ma

• #### OK, my mistake. (Score:2)

You raise a valid point. I was so intent on the font aspect that I didn't see your take on it. Thanks! (sig line notwithstanding - this is an irony-free post.)

on Friday April 18, 2014 @09:16AM (#46787169)

Monospaced font for numbers, so they can line up in a column

• #### zeroes (Score:3, Insightful)

by Anonymous Coward

Monospaced font for numbers, so they can line up in a column

Also: slashed zero, as well as some distinction between capital-i and small-l (el).

A good test string that I ran across was "Illegal1 = O0". Also, m/rn/rri (em/ar-en/ar-ar-eye), w/vv (double-u/vee-vee):

https://en.wikipedia.org/wiki/IDN_homograph_attack

• #### Re: (Score:2)

I really wish I had mod points for this.
• #### Additictive drug for mathematicians (Score:2)

Typeface work is an addictive drug for mathematicians. Look at the decade lost by Knuth on this....ugh.
• #### Bill Meyer's negative space cipher (Score:2)

It sort of reminds me of Bill Meyer's negative space cipher [pineight.com].
• #### Meh. (Score:2)

Why don't people develop new typefaces to represent concepts in programming so we can have better character identifiers for concepts that we need to type out?

• #### Conveyor belt problem... (Score:2)

Interesting article, but I don't understand why the conveyor belt problem (as described) is unsolved. Start with one pulley. Obviously a band around it works. Assume a solution exists for some finite number of pulleys, N. Since the support of the pulley locations is compact, one can always and uniquely determine the exterior of the spanning belt. Place an additional pulley exterior to this belt. There are only three topologically relevant cases -- (an pair of in the case of more than two of) the "near

• #### Re: (Score:1)

The paper that they cite is not in English (Abellanas, "Conectando puntos: poligonizaciones y otros problemas relacionados"), so I am not sure that I even really understand what the statement of the problem is. That being said, I don't think that the induction works out the way you want it too. Consider, for example, a situation in which you add a new pulley to an existing configuration and the two nearest neighbors are separated from the pully added by induction by a stretch of conveyor belt that runs be
• #### Re: (Score:1)

Man, that second sentence is awkward. I should have edited.

Suppose that there exists a configuration of N pulleys. To this configuration, we add an additional pulley. The two pulleys that are nearest to this new pulley are separated from the new pulley by a segment of conveyor that runs between two additional pulleys that are (potentially) quite distant. This configuration provides a counter example to the induction suggested above.

• #### Re: (Score:2)

Why? The only issue is the belt convexity. If the new pulley would pull the belt away from the intermediate pulley if it ran on the outside one can simply switch it to the inside. It cannot be pulled away on both sides. The point is that the run of the belt can be made topologically equivalent to a line drawn between all of the pulley centers in the configuration generated by a distance-ordered recursion from any starting point. All one has to prove is that for a trivial set of local geometries, one ca

• #### The irony... (Score:2)

...is that every scalable font is rendered using computational geometry. All curves in characters are defined with three or more points, and your computing device of choice does a lot of math to render pretty little characters for you.