Maths glyphs in a non-maths font?

Wei Huang

ƒ~∞∫Ω∆∏∑√µ∂◊|¦

These are some glyphs in Adobe Latin 3, particularly math-related, which I don't know the context of their uses and have had to follow the example of other fonts. I've done too much guessing at rationales that may themselves be wrong since there is so much variance in how they're designed?

With some Wikipedia research I found some possible contexts of their uses but I'd be curious to know from others what is the most 'correct' way to design these glyphs and how they are used?

1. ∏∑ sometimes these glyphs are descending below baseline, and ascending just beyond number/cap height, other times they match the number/cap height and start from the baseline.
2. ∫ is even taller the above? sometimes not?
3. ∞ I see these quite small sometimes, other times larger, which look balanced between two numbers.
4. ~ These are sometimes aligned to the top of numbers, sometimes vertically centered, sometimes different again to ≈ (i.e. not merely the component used to make ≈)?
5. √ sometimes there's a horizontal stroke on the left, sometimes it's perpendicular to the first \ stroke down, sometimes the top right has a horizontal stroke? Sometimes it reaches below the baseline, and/or up above the number height?
6. ∂ This glyph just f**** me up
7. ◊ Sometimes it's a full height diamond, sometimes it's a little rotated square?

Also another question I wonder about is how and when would one actually use these glyphs in an Adobe-Latin 3 font if it is not actually suitable for extensive maths typesetting (since it's missing the rest of the glyphs — but what's the point of including some of these maths glyphs then)? 

√172

±√1 −√a

∫ f(x)dx ∫2x

ƒ/2.8

◊(S)

A∆B X∆Y ∆x ∆y ∆ƒ

Ω(G)

∂z ∂x ∂(x) ∂{x} ∂[x] ∂¹ ∂² ∂³ ∂

∞<∞>∞≥∞≤∞

This is a great document detailing some issues to consider in a maths typeface.

Craig Eliason

8. Which of these should acquire a slope in an italic?

Wei Huang

@Frode Bo Helland

Note that there might be differences depending on the intended use of the typeface.

Like what?

ƒ When used as a florin, always italic. When used as a hooked f, follow the lowercase letters.

So, this is a case when two different... letters?glyphs?characters? are in the same slot?

PabloImpallari

I also added /emptyset to my lastest fonts

Nick Shinn

I slope all the math symbols in italic fonts.

I reason that as none of my typefaces are special math fonts, they will not be used for complex math typography.

If typographers want them to be correct, they can switch to the upright, roman font because, after all, many equations are a mixture of roman and italic.

And it is quite likely that the character + will appear in non-mathematical usage, such as the name of a business product, e.g. Google+, or instead of the ampersand in, for instance, London restaurants: Peg + Patriot, Sager + Wilde, Jackson + Rye etc.

As another example, imagine that Einstein’s famous equation E=mc² is text in an all-italic sidebar. In this typical situation, doesn’t it make more sense for the = symbol to be slanted? Because this is just as likely a usage of = in an italic setting as pure maths, if not more so.

attar

> Also another question I wonder about is how and when would one actually use these glyphs in an Adobe-Latin 3 font

Afaict Adobe put these in their charset because they are on Apple keyboard e.g. Option+w is ∑.

Nina Stössinger

Frode Bo Helland said:

| ¦ It’s in the name – vertical bar

:-|

(Which I mean as a clever way of saying, people use these in ways that makes sense to slope them. Especially in typefaces that one wouldn’t expect to be used for hardcore math)

Brandon Schoech

ƒ is used in photography to indicate aperture (f-stop), e.g. ƒ/4.

∫ ∏ ∑ and especially ∂ are more trouble than they’re worth for a non-math font.

I wonder if the little nub on the √ is sometimes left off to make it more usable as a check mark. I remember my old Amiga used this symbol (with nub) as a check mark in program menus.

Thomas Phinney

Adrien Tétar said:

> Also another question I wonder about is how and when would one actually use these glyphs in an Adobe-Latin 3 font

Afaict Adobe put these in their charset because they are on Apple keyboard e.g. Option+w is ∑.

Yes, as one of the people involved in creating those character sets, I can attest it is because they were in the MacRoman character set.

During the OpenType conversion of 2000–2002, Adobe chose to treat MacRoman + WinANSI (plus euro, litre and estimated) as their core characters set. So those math symbols are in Adobe Latin 2, as well. IIRC, literally every alphabetic Adobe font has them! Although in the case of say Mythos or Rad they may not match the main font very well....

Ray Larabie

I'm not sure if that's true anymore but when I worked in the video games business, Sony would reject fonts that didn't have those glyphs. That's the only reason I still include them, even in display fonts where I'm certain they'll never be used.

Kent Lew

As another example, imagine that Einstein’s famous equation E=mc² is text in an all-italic sidebar. In this typical situation, doesn’t it make more sense for the = symbol to be slanted? Because this is just as likely a usage of = in an italic setting as pure maths, if not more so.

Here’s a real-world example of such a non-technical setting. (Okay, so it’s not an all-italic sidebar, but same basic idea, I think.)

From TIME magazine, Nov. 2, 2015:



Call me old-fashioned, but I just don’t see anything wrong with the unslanted symbol.

Nick Shinn

Call me old-fashioned, but I just don’t see anything wrong with the unslanted symbol.

Not such an issue in a serif style, where the = fits nicely with the entry-stroke of /m, but would be awkward in a sans. 

The thing is, the correct scientific presentation is: E = mc², with all variables in italic, a space on either side of the equal symbol, and twosuperior upright. As soon as the equation enters non-scientifc usage as shown in the Time example, without the spaces, and with every character in the italic font, it becomes neither one thing nor the other, being both scientifically wrong, and aesthetically flawed.

John Hudson

Nina,

(Which I mean as a clever way of saying, people use these in ways that makes sense to slope them. Especially in typefaces that one wouldn’t expect to be used for hardcore math)

The vertical bar | is not primarily a math character. It is used for a variety of editorial purposes, e.g. to indicate verse breaks in transcriptions of poetry, and is generally expected to be vertical even in italic text.

I don't think there can be a general rule for whether math symbols in italic fonts are slanted or not, simply because there is no such thing as general typography. All typography is specialist, so the decision process needs to consider the kind of typeface one is making and for what kind of text it is intended. If I were making a type that I expected to be primarily used in advertising copy and packaging design, then I would slant the math symbols. If I were making a type that I expected to be used in book or editorial typography, then I would not slant them. [Notably, when I discussed these kinds of questions with Brill, they asked that not even ( ) [ ] { } and other parenthetical signs be slanted in the italic fonts.] 

Denis Moyogo Jacquerye

In some fonts some shapes are too small or distorted because they've been made tabular, legacy of monospace I guess. But they shouldn't be, unless it's actually a monospace font.

Cory Maylett

Some type design conventions are the result of things that have lost their relevance. Sometimes they're just anachronisms that exist for no apparent reason other than it being safer or more comfortable to continue on than to risk change.

Then again the shape of nearly every glyph in a typical typeface is governed to some extent by convention. If the design of a ∂, for example, gets too far away from what's expected, it becomes less functional. Whether or not the ∂ will even be missed when it's not there in most fonts is questionable. Disagreement over it being okay to italicize the thing seems to be more an esoteric question of whether a situationally dubious convention should be followed or abandoned.

Personally, I think it's fine to violate most any design convention that can't be justified by a practical reason persuasive enough to warrant following it. In a math font, typical users will have more well-defined expectations regarding slanted and upright glyphs, which makes following convention more persuasive. In most editorial and display fonts, however, most graphic designers will regard a non-slanted addition symbol in an italic font as being nothing more than an awkward-looking mistake.

Claudio Piccinini

Cory Maylett said:

Whether or not the ∂ will even be missed when it's not there in most fonts is questionable. Disagreement over it being okay to italicize the thing seems to be more an esoteric question of whether a situationally dubious convention should be followed or abandoned.

I pick up this old, very interesting discussion, because I am in the process of deciding the basic character set I want most of my fonts to have.

My question is about the so-called the "Mac symbol substitution characters" (as they are called in Adobe Latin 2)

• Ω uni2126 (Ohm/Omega)
• π pi
• ∂ partialdiff
• ∆ uni2206 (Delta)
• ∏ product
• ∑ summation
• √ radical
• ∞ infinity
• ∫ integral
• ≈ approxequal
• ≠ notequal
• ≤ lessequal
• ≥ greaterequal
• ◊ lozenge

Since I read @Thomas Phinney confirmed they were added in Adobe Latin 2 for this “legacy reason”, if I am not doing an extended Math symbols set for Math typesetting, does it make sense to have the Greek letters? I will always include the most important Mathematical operators, but I can’t see much of use for Ω, π, ∂, ∆, ∏, ∑, √, ∞, ∫.
Especially if I am doing a historical revival of a typeface which did not contemplate these at all. I mean, I can always add them on an upgrade which extends the character set.

Your thoughts?

Thomas Phinney

Well, these characters are part of the basic MacRoman character set, which can be typed directly even on a standard US English keyboard.

Whether that matters to you or your expected users is another question, of course.

For me, I would still keep them part of my standard character set for that reason. I might omit them in some particular circumstances, though.

Andreas Stötzner

I omit the special ch.s (not the operators) in actual display or fun fonts. In all other, if in doubt, include them. The only laborious one to draw is the Omega. And don’t forget the µ does also belong to this group of characters.

Claudio Piccinini

Thomas Phinney said:

Well, these characters are part of the basic MacRoman character set, which can be typed directly even on a standard US English keyboard.

Whether that matters to you or your expected users is another question, of course.

For me, I would still keep them part of my standard character set for that reason. I might omit them in some particular circumstances, though.

Andreas Stötzner said:

I omit the special ch.s (not the operators) in actual display or fun fonts. In all other, if in doubt, include them. The only laborious one to draw is the Omega. And don’t forget the µ does also belong to this group of characters.

Thanks much to both, this was very important for me to clear my mind. I have documented myself and reasoned on this for a while. So I will follow your advice.
I have another question: my stylistic choice has been to make the basic Arithmetic operators as monolinear and of a light weight, to achieve, so to speak, an “armony of contrast” with the modulated style of De Vinne. Would it make sense, except for the micro/mu, pi, Omega and Delta, to have some of the others (∏, ∑, √, ∞, ∫) drawn in monoline fashion as well? I see that ∏ and ∑ are used in algebra, ∂ is for derivatives, so probably it requires to be modulated.

Craig Eliason

My impulse would be that those more "linear" operators could be monoline but those ones in your parentheses, esp. those deriving from Greek caps, should have contrast.

Claudio Piccinini

Craig Eliason said:

My impulse would be that those more "linear" operators could be monoline but those ones in your parentheses, esp. those deriving from Greek caps, should have contrast.

Yes, thanks — after a bit more documentation I see that it seems the general convention. Especially the Greek letters, which should be proper Greek glyphs following the modulation/style of the other alphabetic characters.
A thing that puzzles me a bit is that not even Tiro’s Brill fonts support:

• ∂ partialdiff
• ∏ product
• ∑ summation
• ◊ lozenge
  

But they support:

• ∫ integral

(I already did lozenge, monolinear, now the perplexity remains on these three, as they’d just be for algebra and derivatives).

@John Hudson: What would your advice be on a "non scholar" textsetting/subtitling typeface (not display)?

Thomas Phinney

+1 to supporting lozenge in text fonts as a simple dingbat character that is of some use (option-shift-V on Mac US English keyboard). But you already have that.

Cristóbal Henestrosa

Thanks for reviving this old discussion. I’d like to know what do you think of this particular question, which I think nobody commented:

1. ∏∑ sometimes these glyphs are descending below baseline, and ascending just beyond number/cap height, other times they match the number/cap height and start from the baseline.

I draw product and summation with the bottom part below the baseline (but not as much as a true descender), but frankly I am not sure if this is a good choice and why.

And one other related question: Do you draw differently these Greek-math operators from the corresponding Greek letters? I mean,
— Delta (uni0394) = increment (uni2206)?
— Omega (uni03A9) = Ohm (uni2126)?
— mu (uni03BC) = micro (uni00B5)?
— Pi (uni03A0) = product (uni220F)?
— Sigma (uni03A3) = summation (uni2211)?

John Savard

Cristobal Henestrosa said:

And one other related question: Do you draw differently these Greek-math operators from the corresponding Greek letters? I mean,

— Delta (uni0394) = increment (uni2206)?
— Omega (uni03A9) = Ohm (uni2126)?
— mu (uni03BC) = micro (uni00B5)?
— Pi (uni03A0) = product (uni220F)?
— Sigma (uni03A3) = summation (uni2211)?

It depends on which operator it is. I don't think there's any need to draw mu for micro, or Omega for Ohm, differently from the normal Greek letters. But Sigma for summation is fairly wide, almost square, while the normal Greek capital letter would not have that shape.

To know what these symbols should look like, it is useful to familiarize oneself with some examples of mathematical typesetting.

K Pease

If you do expect to be setting any calculus, the increment (2206) is expected to be strictly a triangle. For instance, if the text style gives the alphabetical Delta any manner of serifs, you would not want them on the mathematical one. Also, it is not uncommon for the symbol to fall short of the cap height, giving it about the same color as a lowercase letter. But there is very little chance that making it identical to the Delta would be perceived as wrong per se.

Claudio Piccinini

Thanks everyone, this is getting more and more interesting and very helpful for making decisions.

Thomas Phinney said:

+1 to supporting lozenge in text fonts as a simple dingbat character that is of some use (option-shift-V on Mac US English keyboard). But you already have that.

Yes, that’s the reason I always include it, I often use it as a bullet. But again, some professional fonts which support even the algebra operators or the Math Greek letters do not include it!

John Savard said:

Cristobal Henestrosa said:

And one other related question: Do you draw differently these Greek-math operators from the corresponding Greek letters? I mean,

— Delta (uni0394) = increment (uni2206)?
— Omega (uni03A9) = Ohm (uni2126)?
— mu (uni03BC) = micro (uni00B5)?
— Pi (uni03A0) = product (uni220F)?
— Sigma (uni03A3) = summation (uni2211)?

It depends on which operator it is. I don't think there's any need to draw mu for micro, or Omega for Ohm, differently from the normal Greek letters. But Sigma for summation is fairly wide, almost square, while the normal Greek capital letter would not have that shape.

To know what these symbols should look like, it is useful to familiarize oneself with some examples of mathematical typesetting.

Great reply, John. Yes, I believe it depends on tradition or conventions in Math, and clearly Summation and Product are not supposed to sit on the baseline and be identical to /Sigma and /Pi Greek. But then, is there a consolidated historical model to follow as far as height and positioning go?

K Pease said:

If you do expect to be setting any calculus, the increment (2206) is expected to be strictly a triangle. For instance, if the text style gives the alphabetical Delta any manner of serifs, you would not want them on the mathematical one. Also, it is not uncommon for the symbol to fall short of the cap height, giving it about the same color as a lowercase letter. But there is very little chance that making it identical to the Delta would be perceived as wrong per se.

Thanks much for the consideration: so a serifless Delta would be preferable? But I guess it would be the only Greek glyph to be used in mathematics to require formal differentiation, then?
I mean, more than “serif vs. sans serif" it seems to me that here there is at play an expectation of having Greek letters for Math drawn in a certain default style rather than following the overall design logic.

Claudio Piccinini

P.S. Here’s how Product and Summation are used, so they are expected to be centered vertically with the x-height, and be at least two times the Capitals in height.

John Savard

By a strange coincidence, your random example of mathematical typography happens to be evocative of one of the most profound identities in mathematics, the two possible definitions of the Riemann zeta function:

which allow the tools of mathematical analysis to be brought to bear on the properties of the prime numbers.

Claudio Piccinini

Here’s how I decided to design the Product and Summation, to differentiate them from Pi and Sigma and also to make them closer to the monolinear Math operators, I made them lighter:


The corresponding Greek letters, matching the weight and modulation of the Latin letters:

John Savard

Mathematics... in De Vinne??!! For some reason, that seems... strange to me.

Andreas Stötzner

Claudio, the idea of making summation and product a bit lighter is an interesting one. Have you considered to also give the radix a similar contrast (and perhaps a descending stretch)?

I would try out to give the horizontal part of your Delta a little more thickness.