Minion Math — The Design of a New Math Font Family
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Küster, Johannes
“Minion Math” is a set of mathematical fonts I have developed over the past 6 years. Designed as an add–on package to the Adobe MinionPro fonts, it consists of 20 OpenType fonts (4 weights, times 5 optical sizes). In future releases it will cover the complete Unicode math symbols, and more. In the design I tried to avoid all flaws and shortcomings of other math fonts, with the aim of creating the most comprehensive and versatile set of math fonts to date. In this presentation, I will talk about the design principles for Minion Math, and the design decisions I took. I will also show many samples of the fonts and will compare them to other math fonts as well.
 Okay, what I am talking here today about is Minion Math, a family of mathematical fonts I have designed over the past six years. In the design of Minion Math, my design goals were that I wanted to have a math font that really improves over the existing math fonts. I wanted to have a math font family which is completely consistent. For example, with computer modern we have some AMS symbols from the AMSA and B fonts which don't completely match the design of computer modern. So I really wanted a consistent set of math fonts. Should be comprehensive or complete. That I have more glyphs available than other fonts. With complete unicode support, this means nowadays of course. Should be versatile, so with less limitations than other fonts. For example, I didn't want to have the math extension font available only in one width and one optical size and one weight. And I tried to identify all the shortcomings and flaws and constraints in other math fonts known to me and tried to avoid them in the design. So why did I choose Minion? Well first of all I like it and I had it on my mind for a long time to design math fonts for it as well. Originally Minion appeared I think in 1990 as a Post-Crypt font designed by Robert Slimbach of Adobe Systems. It appeared as a multiple master font but still without Greek letters and only with the open type version which appeared in 2001 or 2002. The Greek letters were added to Minion. Actually in a book quite known about typographers, Robert Brinkhurst, the Elements of Typographic Style, there was already shown a sample of a prototype Minion Greek but only with the open type version the Greek appeared. And of course Greek letters are very important for mathematics and when I started on the design I wasn't prepared to design a whole text font or even to add Greek letters to Minion that seemed too complicated for me as a design issue. So I was very glad when Minion appeared with Greek letters in the open type format. And the other strong point of Minion, Minion OpenType appeared with four optical sizes right from the beginning. In the top line you could see the four sizes that Minion offers and the bottom line is the same without sizes. So this here is the regular size and here the regular size is scaled and in the top line you could see the four optical sizes and I think even with the sphemis visible that it really makes a difference. In normal typography optical sizes are nice to have but you could do without but in math they're really crucial for really good mathematics, math typography. So what I started out with were what Minion offered then. Just as I told you with the four optical sizes this place up had regular intercaption and Minion came with three weights in the beginning. So it started to add math characters to these 12 fonts. Shortly after I think in 2004 Adobe issued an update with an extra weight medium between regular and semi-build. It's not that much difference visible between regular and medium but still it is a bit of a difference and so I decided to support medium as well. But in math we need two sizes below regular for script size and script script size. So I decided to add a fifth optical size tiny and so now I ended up with 20 fonts in these five optical sizes now in these four weights and I do fully support these 20 designs. Just to give you an impression of the weights, different weights and the color or grayscale, the visual impact of the symbols. This is our two formulas shown in regular then in medium I go back to regular. So regular and medium is not that much difference but I think you could notice it that the equal sign and the arrow below the limb and so on all have the same visual impact on color grayscale on the page. Then semi-build and build. The X2 one here below is the caption size of course and this one this is the regular size and here again is the optical size caption. So currently the fonts are in a state in which I could release the fonts now. Of course they are commercial fonts because they do depend on Minion and I have used original shapes from Minion. But the fonts are by no means finished. I am aiming of course at complete unicode math support. I have designed most of the glyphs but I would like to review many of them so I won't release them in the first release now. So far I have concentrated on the symbols and didn't do much work on the math alphabets so what I will design later on is a complete fractur and formal script and sans serif. And whatever else is in the unicode blog mathematical alphanumerical characters. And what I will design I experimented a bit on it already. It's a real math italic. This is a feature that only computer modern had for many years that the italic characters for math are designed or cut differently than for text. They have wider, more visible italic characters for math. And I think Cambria was only the second font to implement this feature. I am not sure about sticks where the sticks has really italic math italic characters. In most fonts only the kerning and the side bearings are different so that italic characters have a single character in math and not like in text. But I am planning to add a real math italic which is wider than the normal italic. So the design principles for minion math. What I told you before consistency I tried to achieve complete consistency in shape, size and color. For example the asterisk here matches minion, then the blackboard build which is designed already with all uppercase letters matches minion. Of course it's minion more or less taking apart and added a second stroke. The four Hebrew characters used in math do match minion the Weierstrass P here. Here with the six Greek lowercase characters actually four of them are original minion and two of them I've added. Could you see which were originally a minion and which were added by me? I hope it's not visible. Then the infinity sign, the first epsilon here was added and the second row isn't in minion like this so I've added these two. And of course the summation sign and the integral sign and so on. As I told you I'm planning to have complete unicode math support in the future. This is just an extract from the fonts in my production version or in my development version. So in the first release version not all of these glyphs will be available already but as I told you I've designed most of them already. This is meant to be rather impressive than readable now. So I tried to avoid the constraints of other math fonts. So I will have open type fonts. I haven't added yet the math table for open type fonts but of course I will do that. Then as I told you I have four weights and five optical sizes and each and every glyph is designed in 20 versions and available in 20 versions. Then I didn't stick to the model of tech with only four larger sizes of delimiters but actually I took the idea from the new math encoding that Ulrich talked about this morning. So with traditional old math tech I have only four sizes for 10 point basic delimiter. I have 12, 18, 24 and 30 point delimiters and I added intermediate sizes. I have 15, 21, 27 as well and for parent thesis it goes above that with another seven shapes before I have to resort to sticking them together from pieces. On the left actually there's an error in my PDF. I wanted to show that these are composed of pieces of course like in tech but again I do have seven sizes before I have to resort to putting them together from pieces. And of course I do have many variant glyphs. Just a few samples in the bottom and of course there are many more. In open type they should be accessed by open type features then. Actually they are all encoded in the poor private use area but only for technical reasons or tech reasons they could access them in old fashioned tech encodings but in the future there's no need for poor encodings for all these characters of course. And of course there are many, many details and detailed decisions involved. Here I'm sorry I didn't find time to really finish that table. Unicode defines seven sizes of geometric symbols and the symbols are scattered all over the place in Unicode. The tiny size is actually only usable for the center dot, the C dot. So that's the only symbol here because a white center dot or a white square wouldn't make sense or even a black square wouldn't be recognizable against the C dot. And then there's a very small, medium, small, medium, normal and large size. What Unicode doesn't tell us about is the vertical positioning of the glyphs and when preparing this presentation I didn't find enough time or it didn't get around to do that properly. I decided that the medium size should match the operators so that a medium circle looks like a circle times, O times symbol just without the times. So the medium, medium, small, small, very small and tiny are all centered on the math axis. And the normal size for squares they do sit on the baseline in my design and the large goes a bit below the baseline a bit like a big operator. So there are many more shapes and I decided that for most shapes I will add six sizes, so large from size one large to size six, very small and tiny is only the center dot but I will have circles, black and white and squares, diamonds, liaisances, triangles, of course they're left and right triangles as well and elliptical shapes and rectangles and so on and all these will be available in six sizes in my fonts even if they are not encoded in Unicode. So for the operators, the related and junked symbols I tried to have a consistent look all over. Some of these shapes I don't like in other math fonts, they often like to look too stacked and they visibly fall apart and I tried to have a consistent shape throughout. And in particular these circle shapes I think are much too large in many other math fonts. I think sticks are too big or too large in the sticks fonts and in Cambria math I think they got it utterly wrong. I think such an O plus, a circle plus should look just as large as a plus with a circle around it and not with a much larger circle. Actually Ulrich Viet has this brochure about Cambria math and you could see how the shapes look in Cambria and I think in the back cover, on the back cover Ulrich. Page three of the covers. There are some circle shapes and I think they are much too large. Barbara? Yes, but in Cambria the basic size, the binary operator is too large. In sticks I'm not sure because with the organization of glyphs and sticks I don't know which is which. About arrows I have two remarks. Of course the bar of an arrow is just the basic stroke width of your other math symbols but I think the arrowhead should really match somehow your text font and the obvious candidate to design an arrowhead upon is the French quotation marks, the guimise. So I took that from Minion as a model, of course I had changed it a lot but the arrowheads really do match Minion and look quite Minionic now. And the other remark is that the basic width of arrows is taken too small in many math fonts so the basic arrow is too narrow to have room for all these embellishments that appear on other arrows and I think the basic arrow should be wide enough so you don't have to change the metrics to have all these other arrows. Of course you could have wide arrows as well but the basic size should be consistent throughout. And then of course the diagonal and up and down arrows. Actually the arrowhead is different for up and down arrows than from left and right arrows and also different in diagonal arrows. I think you can't notice it here but if you turn the arrow around you could see it. One of my main remark here is that the diagonal shapes are in my opinion too large in many fonts. On the left here is shown computer modern with the left to right the up and two diagonal arrows overlaid and on the right is my design for Minion and here in computer modern the diagonal arrows are obviously drawn in a square and here I try to draw them rather in a circle and I think it looks much better. Normally the diagonal arrows look much too large in computer modern I think. So negated symbols in original Minion this is the not equal which is included in original Minion. I think the slant is just too much it's too sloped and then the negation slash is also too short. So I completely redesigned the symbol in Minion math and this has the advantage that I could keep the same slope all over the negated symbols of course with some obvious exceptions here in the bottom where I couldn't keep the slope. Here I tried to have the same slope then the symbol doesn't look negated at all it looks like a new symbol but not like a negated symbol and also with the size of the negation slash I could keep the same size for many symbols only for more stacked symbols I need to change that to a larger size. So again I get more consistency all over the fonts and most of the negated symbols look clearly like negated symbols while when I have this slash then for less sign I would have to apply a different slope then it gets more confusing. Then some characters in original Minion aren't usable for math so the italic new or new and the V aren't different at all in Minion so that's Greek and that's Latin and of course within a word it doesn't make a difference or it's recognizable of course but with in math you need two different shapes so you completely redesigned these. So now the new or new in Minion math looks like this and the V looks like this and matching to the round V I of course need a matching round W. And of course mathematicians do like some very strange letters. I think I've seen it in use only in two or three of my math books but of course every math font needs to have this V. And here again I try to model it as closely as possible on Minion. You could see some of the Minion letters I used to model the Vajashtras P upon. So the beginning is taken from the upright omega and here the loop in the bottom is from the VARP and here that's taken from the S a bit and changed and of course here it's taken from the italic B. I'm still not completely satisfied with the look of that loop here in the bottom but at least the metrics are fixed for this character and maybe I could change the shape a bit later on and of course the depth of the descender here is taken from the italic F so it really matches Minion in all aspects or as good as possible. Yet another issue is the asterisk. I think it should also match the text font. Of course it should always have this form so it should always be a six pointed star and not a five pointed star or anything else. And of course it should have one vertical stroke and two cross strokes then. The reason why mathematicians have this predilection for six pointed asterisk is of course handwriting because handwriting you could do it like this and a five pointed star in handwriting is not doable that easy. It really should be six pointed always. And of course to match Minion I modeled it on the dagger and double dagger and of course the additional symbols using the asterisk use the same shape as well so the circled asterisk and the big operator which is also added in the font. I think it's not a unicode character yet. I'm not sure. I think it's a quite a published example. But it has to be a math book or does a typography book count as well? Okay. I'm just going to call this one as a little source. Okay. Of course I used it in a typography book already. And if we could click like that into the examples. Yes. Okay. So this is the example from the LaTeX companion which is shown in many math fonts and here it's computer modern and then this is how it looks in Minion math. Should I go back again? For example in computer modern I think the summation sign is a bit too bold. It's not that visible here but in many books it really looks too blotchy on the page. And this is Minion again, Minion math. And I do have a third sample of Fourier and Utopia. Utopia is another font designed by Robert Slimbeck of Adobe just like Minion and Utopia was designed by some French. Thank you. Here again it's Minion. Actually I haven't worked enough on the kerning yet so it could be improved in some places. What I do have is a basic size of these moustache characters but not yet in the larger sizes. So here in computer modern it's too large and here it's too small. And I haven't worked yet on the alphabet so that's just from the RSFS form script font. So some more samples from test math to testmov.tech, the sample file from the AMS math package. But I think it's time for questions and you could look at the samples during the questions then. Okay, thank you. Thank you. Good evening. Nice tovl0e terug, in character and melody. And as Paul Francis pointed out, things like that can get into the music zone, standards have to be shown to be new, to a particular different kind of stress. We... Therefore, mass thought designers should not be restricting their recovery up to the use of a thought. Obviously we need representation of new codes or obstacles that are going to create in the future. For example, in the area of math alphabet, math physicians would use lots more math alphabet than will anyway. It would be nice to have them in the... in the... in the form of the... I mean, Paul would know the history of it, but the particular ones that have happened to end up in the code form with some of the triumphant... in that two-room, Barbara. It's somewhat arbitrary. Yeah, okay, somewhat arbitrary, for the career. I mean, I assume that... I assume that math paper has five different script fonts. Now, unit code is not 1007, it's... Why not? I'm not sure. Just to give one more example, we had your big... big alphabet, then maybe Barbara's right, but I know what it means. Yeah. Exactly what it means. And math and math supports the idea of having it. If you see what I mean. Well, I have added all obvious variations, or will add all obvious variations in the private use area. So, for example, unit code, for some areas, only codes the left-to-right version, and of course I have a right-to-left version or a double-head version, wherever it makes sense. And... I have double diagonal arrows with two heads, double-head diagonal arrows, which goes in the pur as well. All the larger sizes of big operators and of parent visas or delimiters, and so on. I do have a symbol for greatest common divisor and least common multiple, which goes in the pur as well. A new kind of delimiter. And so on and so on. And some small... Yeah, for example, for the circled symbols, I will have a circled plus with a white rim, so that the plus doesn't touch the circle, also in the pur and so on. So, I'm trying to add all the math characters I could think of. I think my correct answer to that is that the math and the algorithm are actually coming up in a way that directly exists, but we don't have to... Okay. Let's just take one more question and let's get down there. You have a quick question. What's the legal path? Do we have Adobe Class? Yes, I do have an agreement with Adobe now. So I got licensed for fonts. And I'm licensed to use the name Minion. So Minion is the trademark of Adobe Systems, or just a trademark and used by permission. And... What, is that a mark? They had already, yes. Okay. Okay. Okay. Thank you.
 Okay, what I am talking here today about is Minion Math, a family of mathematical fonts  I have designed over the past six years.  In the design of Minion Math, my design goals were that I wanted to have a math font that  really improves over the existing math fonts.  I wanted to have a math font family which is completely consistent.  For example, with computer modern we have some AMS symbols from the AMSA and B fonts  which don't completely match the design of computer modern.  So I really wanted a consistent set of math fonts.  Should be comprehensive or complete.  That I have more glyphs available than other fonts.  With complete unicode support, this means nowadays of course.  Should be versatile, so with less limitations than other fonts.  For example, I didn't want to have the math extension font available only in one width  and one optical size and one weight.  And I tried to identify all the shortcomings and flaws and constraints in other math fonts  known to me and tried to avoid them in the design.  So why did I choose Minion?  Well first of all I like it and I had it on my mind for a long time to design math fonts  for it as well.  Originally Minion appeared I think in 1990 as a Post-Crypt font designed by Robert Slimbach  of Adobe Systems.  It appeared as a multiple master font but still without Greek letters and only with the  open type version which appeared in 2001 or 2002.  The Greek letters were added to Minion.  Actually in a book quite known about typographers, Robert Brinkhurst, the Elements of Typographic  Style, there was already shown a sample of a prototype Minion Greek but only with the  open type version the Greek appeared.  And of course Greek letters are very important for mathematics and when I started on the  design I wasn't prepared to design a whole text font or even to add Greek letters to  Minion that seemed too complicated for me as a design issue.  So I was very glad when Minion appeared with Greek letters in the open type format.  And the other strong point of Minion, Minion OpenType appeared with four optical sizes  right from the beginning.  In the top line you could see the four sizes that Minion offers and the bottom line is  the same without sizes.  So this here is the regular size and here the regular size is scaled and in the top  line you could see the four optical sizes and I think even with the sphemis visible  that it really makes a difference.  In normal typography optical sizes are nice to have but you could do without but in math  they're really crucial for really good mathematics, math typography.  So what I started out with were what Minion offered then.  Just as I told you with the four optical sizes this place up had regular intercaption and  Minion came with three weights in the beginning.  So it started to add math characters to these 12 fonts.  Shortly after I think in 2004 Adobe issued an update with an extra weight medium between  regular and semi-build.  It's not that much difference visible between regular and medium but still it is a bit of  a difference and so I decided to support medium as well.  But in math we need two sizes below regular for script size and script script size.  So I decided to add a fifth optical size tiny and so now I ended up with 20 fonts in these  five optical sizes now in these four weights and I do fully support these 20 designs.  Just to give you an impression of the weights, different weights and the color or grayscale,  the visual impact of the symbols.  This is our two formulas shown in regular then in medium I go back to regular.  So regular and medium is not that much difference but I think you could notice it that the equal  sign and the arrow below the limb and so on all have the same visual impact on color  grayscale on the page.  Then semi-build and build.  The X2 one here below is the caption size of course and this one this is the regular  size and here again is the optical size caption.  So currently the fonts are in a state in which I could release the fonts now.  Of course they are commercial fonts because they do depend on Minion and I have used original  shapes from Minion.  But the fonts are by no means finished.  I am aiming of course at complete unicode math support.  I have designed most of the glyphs but I would like to review many of them so I won't release  them in the first release now.  So far I have concentrated on the symbols and didn't do much work on the math alphabets  so what I will design later on is a complete fractur and formal script and sans serif.  And whatever else is in the unicode blog mathematical alphanumerical characters.  And what I will design I experimented a bit on it already.  It's a real math italic.  This is a feature that only computer modern had for many years that the italic characters  for math are designed or cut differently than for text.  They have wider, more visible italic characters for math.  And I think Cambria was only the second font to implement this feature.  I am not sure about sticks where the sticks has really italic math italic characters.  In most fonts only the kerning and the side bearings are different so that italic characters  have a single character in math and not like in text.  But I am planning to add a real math italic which is wider than the normal italic.  So the design principles for minion math.  What I told you before consistency I tried to achieve complete consistency in shape,  size and color.  For example the asterisk here matches minion, then the blackboard build which is designed  already with all uppercase letters matches minion.  Of course it's minion more or less taking apart and added a second stroke.  The four Hebrew characters used in math do match minion the Weierstrass P here.  Here with the six Greek lowercase characters actually four of them are original minion  and two of them I've added.  Could you see which were originally a minion and which were added by me?  I hope it's not visible.  Then the infinity sign, the first epsilon here was added and the second row isn't in  minion like this so I've added these two.  And of course the summation sign and the integral sign and so on.  As I told you I'm planning to have complete unicode math support in the future.  This is just an extract from the fonts in my production version or in my development  version.  So in the first release version not all of these glyphs will be available already but  as I told you I've designed most of them already.  This is meant to be rather impressive than readable now.  So I tried to avoid the constraints of other math fonts.  So I will have open type fonts.  I haven't added yet the math table for open type fonts but of course I will do that.  Then as I told you I have four weights and five optical sizes and each and every glyph  is designed in 20 versions and available in 20 versions.  Then I didn't stick to the model of tech with only four larger sizes of delimiters but actually  I took the idea from the new math encoding that Ulrich talked about this morning.  So with traditional old math tech I have only four sizes for 10 point basic delimiter.  I have 12, 18, 24 and 30 point delimiters and I added intermediate sizes.  I have 15, 21, 27 as well and for parent thesis it goes above that with another seven shapes  before I have to resort to sticking them together from pieces.  On the left actually there's an error in my PDF.  I wanted to show that these are composed of pieces of course like in tech but again I  do have seven sizes before I have to resort to putting them together from pieces.  And of course I do have many variant glyphs.  Just a few samples in the bottom and of course there are many more.  In open type they should be accessed by open type features then.  Actually they are all encoded in the poor private use area but only for technical reasons or  tech reasons they could access them in old fashioned tech encodings but in the future  there's no need for poor encodings for all these characters of course.  And of course there are many, many details and detailed decisions involved.  Here I'm sorry I didn't find time to really finish that table.  Unicode defines seven sizes of geometric symbols and the symbols are scattered all over the  place in Unicode.  The tiny size is actually only usable for the center dot, the C dot.  So that's the only symbol here because a white center dot or a white square wouldn't make  sense or even a black square wouldn't be recognizable against the C dot.  And then there's a very small, medium, small, medium, normal and large size.  What Unicode doesn't tell us about is the vertical positioning of the glyphs and when  preparing this presentation I didn't find enough time or it didn't get around to do  that properly.  I decided that the medium size should match the operators so that a medium circle looks  like a circle times, O times symbol just without the times.  So the medium, medium, small, small, very small and tiny are all centered on the math  axis.  And the normal size for squares they do sit on the baseline in my design and the large  goes a bit below the baseline a bit like a big operator.  So there are many more shapes and I decided that for most shapes I will add six sizes,  so large from size one large to size six, very small and tiny is only the center dot  but I will have circles, black and white and squares, diamonds, liaisances, triangles,  of course they're left and right triangles as well and elliptical shapes and rectangles  and so on and all these will be available in six sizes in my fonts even if they are  not encoded in Unicode.  So for the operators, the related and junked symbols I tried to have a consistent look  all over.  Some of these shapes I don't like in other math fonts, they often like to look too stacked  and they visibly fall apart and I tried to have a consistent shape throughout.  And in particular these circle shapes I think are much too large in many other math fonts.  I think sticks are too big or too large in the sticks fonts and in Cambria math I think  they got it utterly wrong.  I think such an O plus, a circle plus should look just as large as a plus with a circle  around it and not with a much larger circle.  Actually Ulrich Viet has this brochure about Cambria math and you could see how the shapes  look in Cambria and I think in the back cover, on the back cover Ulrich.  Page three of the covers.  There are some circle shapes and I think they are much too large.  Barbara?  Yes, but in Cambria the basic size, the binary operator is too large.  In sticks I'm not sure because with the organization of glyphs and sticks I don't know which is  which.  About arrows I have two remarks.  Of course the bar of an arrow is just the basic stroke width of your other math symbols  but I think the arrowhead should really match somehow your text font and the obvious candidate  to design an arrowhead upon is the French quotation marks, the guimise.  So I took that from Minion as a model, of course I had changed it a lot but the arrowheads  really do match Minion and look quite Minionic now.  And the other remark is that the basic width of arrows is taken too small in many math fonts  so the basic arrow is too narrow to have room for all these embellishments that appear  on other arrows and I think the basic arrow should be wide enough so you don't have to  change the metrics to have all these other arrows.  Of course you could have wide arrows as well but the basic size should be consistent throughout.  And then of course the diagonal and up and down arrows.  Actually the arrowhead is different for up and down arrows than from left and right arrows  and also different in diagonal arrows.  I think you can't notice it here but if you turn the arrow around you could see it.  One of my main remark here is that the diagonal shapes are in my opinion too large in many  fonts.  On the left here is shown computer modern with the left to right the up and two diagonal  arrows overlaid and on the right is my design for Minion and here in computer modern the  diagonal arrows are obviously drawn in a square and here I try to draw them rather in a circle  and I think it looks much better.  Normally the diagonal arrows look much too large in computer modern I think.  So negated symbols in original Minion this is the not equal which is included in original  Minion.  I think the slant is just too much it's too sloped and then the negation slash is also  too short.  So I completely redesigned the symbol in Minion math and this has the advantage that  I could keep the same slope all over the negated symbols of course with some obvious exceptions  here in the bottom where I couldn't keep the slope.  Here I tried to have the same slope then the symbol doesn't look negated at all it looks  like a new symbol but not like a negated symbol and also with the size of the negation  slash I could keep the same size for many symbols only for more stacked symbols I need  to change that to a larger size.  So again I get more consistency all over the fonts and most of the negated symbols look  clearly like negated symbols while when I have this slash then for less sign I would  have to apply a different slope then it gets more confusing.  Then some characters in original Minion aren't usable for math so the italic new or new and  the V aren't different at all in Minion so that's Greek and that's Latin and of course  within a word it doesn't make a difference or it's recognizable of course but with in  math you need two different shapes so you completely redesigned these.  So now the new or new in Minion math looks like this and the V looks like this and matching  to the round V I of course need a matching round W.  And of course mathematicians do like some very strange letters.  I think I've seen it in use only in two or three of my math books but of course every  math font needs to have this V.  And here again I try to model it as closely as possible on Minion.  You could see some of the Minion letters I used to model the Vajashtras P upon.  So the beginning is taken from the upright omega and here the loop in the bottom is from  the VARP and here that's taken from the S a bit and changed and of course here it's  taken from the italic B.  I'm still not completely satisfied with the look of that loop here in the bottom but at  least the metrics are fixed for this character and maybe I could change the shape a bit later  on and of course the depth of the descender here is taken from the italic F so it really  matches Minion in all aspects or as good as possible.  Yet another issue is the asterisk.  I think it should also match the text font.  Of course it should always have this form so it should always be a six pointed star and  not a five pointed star or anything else.  And of course it should have one vertical stroke and two cross strokes then.  The reason why mathematicians have this predilection for six pointed asterisk is of course handwriting  because handwriting you could do it like this and a five pointed star in handwriting is  not doable that easy.  It really should be six pointed always.  And of course to match Minion I modeled it on the dagger and double dagger and of course  the additional symbols using the asterisk use the same shape as well so the circled  asterisk and the big operator which is also added in the font.  I think it's not a unicode character yet.  I'm not sure.  I think it's a quite a published example.  But it has to be a math book or does a typography book count as well?  Okay.  I'm just going to call this one as a little source.  Okay.  Of course I used it in a typography book already.  And if we could click like that into the examples.  Yes.  Okay.  So this is the example from the LaTeX companion which is shown in many math fonts and here  it's computer modern and then this is how it looks in Minion math.  Should I go back again?  For example in computer modern I think the summation sign is a bit too bold.  It's not that visible here but in many books it really looks too blotchy on the page.  And this is Minion again, Minion math.  And I do have a third sample of Fourier and Utopia.  Utopia is another font designed by Robert Slimbeck of Adobe just like Minion and Utopia  was designed by some French.  Thank you.  Here again it's Minion.  Actually I haven't worked enough on the kerning yet so it could be improved in some places.  What I do have is a basic size of these moustache characters but not yet in the larger sizes.  So here in computer modern it's too large and here it's too small.  And I haven't worked yet on the alphabet so that's just from the RSFS form script font.  So some more samples from test math to testmov.tech, the sample file from the AMS math package.  But I think it's time for questions and you could look at the samples during the questions  then.  Okay, thank you.  Thank you.  Good evening.  Nice tovl0e terug,  in character and melody.  And as Paul Francis pointed out, things like that  can get into the music zone,  standards have to be shown to be new,  to a particular different kind of stress.  We...  Therefore,  mass thought designers  should not be restricting their recovery  up to the use of a thought.  Obviously we need representation  of new codes or obstacles  that are going to create in the future.  For example, in the area of math alphabet,  math physicians would use lots more math alphabet  than will anyway.  It would be nice to have them in the...  in the...  in the form of the...  I mean, Paul would know the history of it,  but the particular ones that have happened  to end up in the code form  with some of the triumphant...  in that two-room, Barbara.  It's somewhat arbitrary.  Yeah, okay, somewhat arbitrary, for the career.  I mean, I assume that...  I assume that math paper  has five different script fonts.  Now, unit code is not 1007, it's...  Why not?  I'm not sure.  Just to give one more example,  we had your big... big alphabet,  then maybe Barbara's right,  but I know what it means.  Yeah.  Exactly what it means.  And math and math supports the idea of having it.  If you see what I mean.  Well, I have added all obvious variations,  or will add all obvious variations  in the private use area.  So, for example, unit code,  for some areas,  only codes the left-to-right version,  and of course I have a right-to-left version  or a double-head version,  wherever it makes sense.  And...  I have double diagonal arrows  with two heads,  double-head diagonal arrows,  which goes in the pur as well.  All the larger sizes of big operators  and of parent visas or delimiters,  and so on.  I do have a symbol for  greatest common divisor and least common multiple,  which goes in the pur as well.  A new kind of delimiter.  And so on and so on.  And some small...  Yeah, for example, for the circled symbols,  I will have a circled plus with a white rim,  so that the plus doesn't touch the circle,  also in the pur and so on.  So, I'm trying to add all the math characters  I could think of.  I think my correct answer to that is that the math and the algorithm  are actually coming up in a way that directly exists,  but we don't have to...  Okay.  Let's just take one more question and let's get down there.  You have a quick question.  What's the legal path?  Do we have Adobe Class?  Yes, I do have an agreement with Adobe now.  So I got licensed for fonts.  And I'm licensed to use the name Minion.  So Minion is the trademark of Adobe Systems,  or just a trademark and used by permission.  And...  What, is that a mark?  They had already, yes.  Okay.  Okay.  Okay.  Thank you.
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