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A mathematical delimiter is a symbol used to enclose or separate parts of a mathematical expression, such as parentheses, brackets or vertical bars. Its visible size should suit the enclosed material. Mathematical typesetting can select a larger mathematical glyph variant or construct a mathematical glyph assembly when a default glyph is too small.^[ref]

For example, compare the grouping inThe parentheses enclose the complete typeset fraction, so its height and depth inform their layout. The superscript applies to the grouped expression. In TeX, \left( and \right) request paired size-sensitive delimiters around the enclosed material. The stored parenthesis characters can therefore yield different glyphs in different formula contexts.

The Math axis provides a useful alignment reference for symmetric enclosing shapes. A font's choice of larger variants or assembly parts can preserve appropriate stroke weights and proportions while the expression grows.

A mathematical font constant is a font-specific parameter used in mathematical typesetting. The MathConstants portion of an OpenType MATH table supplies distances, percentages and other parameters, including the Math axis offset and script scaling.^[ref]

For an invented distance example, suppose a computer font uses 1000 font units per em and specifies fractionRuleThickness as 40 font units. At 25 pixels per em, the ideal typeset fraction bar thickness isAt 50 pixels per em, the same stored value gives 2 pixels before rasterization adjustments. A percentage value such as 80, however, is a ratio and must not be converted as though it meant 80 font units.

Keeping the units explicit prevents plausible-looking scale errors. Suggested values in the specification guide font design; they are not universal dimensions shared by every computer font.

Mathematical typesetting arranges symbolic expressions in two dimensions. It must coordinate computer fonts, glyph positioning, typesetting boxes and text baselines while preserving the expression's visible structure. A typeset fraction positions its components above and below a bar; superscripts, subscripts, square roots and mathematical delimiters impose other geometric relationships.^[ref]

For example,contains a superscript inside the upper component and a square root inside the lower component. Their dimensions help determine the height of the complete typeset fraction. A larger expression may then require larger surrounding mathematical delimiters. Laying out the smallest parts first makes this a recursive geometric construction.

An OpenType MATH table supplies font-specific information such as placement constants and suitable glyph variants. The table supplies data for layout; different implementations can use those data in different algorithms. TeX and LaTeX provide established authoring systems for expressing such mathematical structure.^[ref]

The mathematical typesetting axis, or Math axis, is a horizontal alignment reference for a formula. Its offset from the text baseline is a mathematical font constant, represented by axisHeight in an OpenType MATH table.^[ref]

For an invented coordinate example, choose upward-positive coordinates, put the text baseline at $y=0$, and set the axis offset to $a=250$ font units in a computer font with 1000 font units per em. At 20 pixels per em, the axis is $250(20/1000)=5$ pixels above that baseline. A symmetric enclosing shape spanning $y=-350$ to $y=850$ has midpoint $250$, so its centre lies on the axis.

The typeset fraction bar is another useful alignment cue. The reference fixes relative placement; translating the whole formula also translates its baseline and axis.

A mathematical typesetting style selects layout conventions appropriate to a formula's context, including compact inline material and more spacious displayed material. In MathML, math-style distinguishes normal and compact, while math-depth participates in nested size selection.^[ref]

Compare two presentations of the same expression:Both represent the same quotient, but reserve different vertical space. In TeX, \displaystyle and \textstyle request these contexts. The choice matters when fitting a typeset fraction into a line without making neighbouring text baselines unnecessarily far apart.

For a hypothetical computer font with first- and second-level script scales 80 and 60 percent, a base font size of 20 units gives script sizes 16 and 12. The second value is relative to the base, so it is not $0.8^2(20)=12.8$. Actual percentages come from the computer font's mathematical font constants.^[ref]

MathML is a markup language for mathematical notation, structure and content on the web. Its elements describe expressions within a document rather than reducing a formula to a flat character string. MathML Core specifies a subset suited to web browser implementation; the cited 24June2025 document is a Candidate Recommendation Snapshot.^[ref]

Consider the typeset fraction $\frac{x+1}{2}$. A presentation encoding is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac></math>. The mi, mo and mn elements identify a symbolic name, an operator and numbers. The mrow groups the numerator; the two children of mfrac provide the numerator and denominator.^[ref]

Grouping changes the represented expression. At $x=3$, the intended fraction gives $(3+1)/2=2$, whereas $x+1/2=7/2$. This arithmetic illustrates the meaning assigned to the structure; MathML presentation markup does not itself execute the calculation. Maintaining a structured representation helps document tools manipulate a formula and lets layout follow its mathematical grouping.

MathML Core is a browser-oriented subset of MathML with specified rules for mathematical presentation and layout. The pinned 24 June 2025 document is a Candidate Recommendation Snapshot. It defines a concrete target for implementation, rather than identifying the whole MathML language with one browser's output.^[ref]

For an original example, encode a typeset fraction surrounded by parentheses as <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo stretchy="true">(</mo><mfrac><mi>x</mi><mn>2</mn></mfrac><mo stretchy="true">)</mo></mrow></math>. The row has three children: a left mathematical delimiter, the typeset fraction and a right mathematical delimiter. The fraction's children supply numerator $x$ and denominator 2.

The parentheses are stretchy mathematical operators: their markup requests size-sensitive layout around the fraction. Core specifies operator stretching and row layout; mathematical glyph variants or mathematical glyph assemblies can supply suitable forms.^[ref] This illustrates why presenting a formula requires more than placing all its characters on one text baseline.

Changing stretchy="true" to stretchy="false" changes the layout instruction without changing the fraction's two operands. Exact dimensions also depend on the computer font and applicable layout properties. The markup supplies structure and presentation instructions; substituting a numerical value for $x$ and evaluating the quotient is a separate operation.

An OpenType MATH table stores font-specific information for mathematical typesetting. Its major components supply mathematical font constants, per-glyph placement information, and data for mathematical glyph variants or mathematical glyph assemblies.^[ref]

For example, a tall typeset fraction can require larger surrounding mathematical delimiters. The font may offer several ready-made parentheses and parts for assembling still taller ones. An implementation can use those data together with the expression's measured dimensions. Merely scaling one outline uniformly could change its stroke weight along with its height; the supplied variants and parts give the font designer more control over the result.

The same general division of labour applies to subscripts and superscripts: a font supplies relevant dimensions and placement information, while the layout process combines them with the actual expression. The table is a data interface used by layout algorithms. It does not uniquely prescribe the complete appearance of every formula.^[ref]

A stretchy mathematical operator can adapt its extent to the surrounding mathematical layout. In MathML Core, an mo element's stretchy property participates in this decision. A mathematical delimiter around a tall typeset fraction is a familiar example. Actual stretching also requires an applicable constraint and suitable computer font data.^[ref]

For an original example, use <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo stretchy="true" minsize="2em" maxsize="3em">(</mo><mfrac><mi>x</mi><mn>2</mn></mfrac><mo stretchy="true" minsize="2em" maxsize="3em">)</mo></mrow></math>. The row places two mathematical delimiters around a typeset fraction with numerator $x$ and denominator 2.

Suppose the positive block-axis target totals, already expressed at a common scale, are $1.5$, $2.5$ and $4$ em. The stated size bounds adjust them to $2$, $2.5$ and $3$ em, respectively. This is the target-size constraint step, not a prediction of exact rendered ink heights. The complete algorithm also handles ascent/descent and symmetry about the Math axis.^[ref]

Suitable mathematical glyph variants or mathematical glyph assemblies can supply the extended form. Setting stretchy="false" changes the operator's instruction without changing the fraction's two operands. Layout properties and font constructions therefore belong in a controlled comparison; enlarging every outline uniformly is not the definition of stretching.