Two math updates have happened: 1) the STIX math fonts have been upgraded to Version 2.0, which works well with Microsoft Word, and 2) Unicode Technical Report #25, Unicode Support Mathematics has been updated to include discussion of slashed-zero and empty-set variations. This post discusses these updates.

## STIX Fonts 2.0

We compare STIX 2 Math (STIX2Math.otf) and Cambria Math in an equation and in an expression with nested parentheses. To make the equation accessible, here’s the Nemeth braille and UnicodeMath for it with math-italic variables mapped to upright for simplicity

⠹⠂⠌⠆⠨⠏⠼ |
⠮⠰⠴⠘⠆⠨⠏⠐⠹⠙⠨⠹⠌⠁⠬⠃⠀⠎⠊⠝⠀⠨⠹⠼ | ⠀⠨⠅⠀ | ⠹⠂⠌⠜⠁⠘⠆⠐⠤⠃⠘⠆⠐⠻⠼ |

1/2π | ∫_0^2π dθ/(a+b sin θ) | = |
1/√(a^2-b^2 ) |

The equation occurs, for example, in mode-locking phenomena in lasers, clocks, tuning forks, and other sustained oscillators. Hence the name “mode-locking equation”. More on that at the end. Here’s the equation in STIX Math 2.0

And here it is in Cambria Math

Many symbols look very similar, but note that the STIX *θ* has wider stems on top and bottom while Cambria Math has wider stems on left and right. The images are snipped from a Word document.

Similarly, here’s the nested parenthesized expression ((((((((a+b)))))))) in STIX Math 2.0

And in Cambria Math

It’s interesting to see how much larger the parentheses become in Cambria Math. The parameters guiding the layout of both are given in their respective OpenType math tables.

Re mode locking, Huygens is probably best known for his wave theory of light, but he was also the one who first put the pendulum into a clock. One day he observed that two pendulum clocks which ticked at slightly different rates when apart, ticked at the same rate when hung close together on the same wall. This mode locking phenomenon can be described, in part, by the equation above (see p. 52 of *Laser Physics*, Sargent, Scully and Lamb, Addison-Wesley, 1974)

## Unicode Technical Report #25, Unicode Support for Mathematics, Version 15

This latest version of UTR #25 includes a discussion of glyph variants for the digit 0 and for the empty-set symbol ∅. Specifically, it notes in Section 2.7 that sometimes, specific glyph forms are chosen by notational style or are needed for contrast with other notation in the same document. For example, the symbol U+2205 ∅ EMPTY SET can be found in its slashed zero-shaped glyph form in documents typeset in TeX that use the command \emptyset, or in contexts where it is contrasted with the semantically distinct slashed digit zero.

For this and certain other well-established glyph variants of mathematical symbols, standardized variation sequences were added to the Unicode Standard. Thus, for example, the standardized variation sequence <U+2205, U+FE00> represents the oval variant of the empty-set symbol. To avoid the misuse of that sequence for the glyph variant of the digit zero with a short diagonal stroke “0”, the standardized variation sequence <U+0030, U+FE00> represents the digit zero glyph variant.

The report also uses the name UnicodeMath to refer to the math “linear format” in Unicode Technical Note #28. Since there are several math linear formats, it’s helpful to use a more precise name for that linear format.