The Art Of Setting Beautiful Yet Readable Math Expressions In Latex
LaTeX provides robust tools for typesetting mathematical expressions. With its vast array of math environments, fonts, sizes, packages and methods for alignment, spacing and textual integration, LaTeX gives the author fine-grained control over the aesthetic presentation of formulas and equations.
At the same time, the primary goal of any technical document is effective communication. Math expressions, no matter how beautiful, lose their purpose if readers struggle to unravel their meaning. Readability, clarity and fluent Parsing must work in tandem with visual appeal to produce math typesetting fit for its purpose.
This article explains key LaTeX capabilities purpose-built for mathematics. It offers guidelines and best practices for leveraging these tools to generate math expressions both pleasing to the eye and readily comprehensible. Note the intricate interplay between aesthetics and clarity in math typesetting. Mastering this balance is key to ensuring that the beauty of your math actively supports rather than opposes the communication of meaning.
Choosing the Right Math Environments
LaTeX math capabilities center around math environments. These are special text formats with syntax rules tailored for mathematical notation. Learning which environment suits which math construct gives the author robust control over expression structure.
Inline math embedded directly in a paragraph uses the math environment. Simple mathematical entities like scalars and short expressions are best typeset inline. The math environment integrates seamlessly into textual discussion of mathematical concepts.
Multiline equations, equation arrays and complex symbolic constructs are better suited to display math environments. These render formulas as floating blocks separate from body text. Key display environments like \begin{equation} and \begin{align} add equation numbers and support alignment of multiline math.
Specialized math environments like matrices and piecewise functions further expand typesetting capabilities. The amsmath package provides still more environments like \begin{cases} for case distinctions.
Learning which environments best frame different mathematical objects fosters clarity through meaningful structure. Consistent and intentional environment choices also contribute to aesthetic uniformity in math expressions.
Example Environments
- Inline math: $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$
- Equation:
\begin{equation}
x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}
\end{equation} - Matrix:
\begin{matrix}
a & b \\
c & d
\end{matrix}
Fonts and Sizes for Optimal Readability
Equation readability depends heavily on symbolic font variations like italics for variables versus roman font for textual operators. LaTeX math environments handle most font styling automatically. Further control is possible by applying math alphabet commands like \mathit, \mathbf and \mathsf.
Font size also impacts readability. Display style math looks best with larger fonts to match body text scale. Inline math styled closer to running text size integrates smoothly. The key is balance through intentional size choices that account for context.
For example, large inline math expressions risk breaking line spacing. Small display equations conversely fail to attract enough attention beside body text. Some manual tuning via commands like \Huge may be necessary to strike the right balance.
Example Font and Size Adjustments
- Variables italicized: $\mathit{x}, \mathit{y}$
- Vectors bold: $\mathbf{v}, \mathbf{w}$
- Larger displaystyle: {\Huge $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$}
- Smaller inline: {$\scriptstyle x = {-b \pm \sqrt{b^2-4ac} \over 2a}$}
Spacing Around Math Expressions
Proper spacing ensures math formulas visually stand out from body text without creating awkward gaps in flow. LaTeX automatically applies some intelligent spacing rules, like spacing out operators relative to operands.
Additional control over math spacing improves polish. In display math, manual spacing adjustments between lines using \\[2ex] directives tidy up vertical rhythm. In inline math, judicious use of spacing commands like \; and \quad dial in inter-symbolic and post-math breath.
Used sparingly and with intent, manual spacing tuning smooths out rough spacing edges. But excessive tweaking risks harming readability through distraction.
Example Spacing Adjustments
- Line spacing in display:
\begin{align*}
x &= 3 + 2 \\[2ex]
y &= 4 - 5
\end{align*} - Inter-symbolic spacing: $a\,b\quad c\;d$
- Post-math breath: $x = y^2$ \quad for all $y$.
Aligning Long Equations Gracefully
Aligning elements in multiline display equations aids comprehension through visual grouping. LaTeX display environments like align, gathered and aligned equipped with & column marks streamline alignment across math lines.
Manual math spacing tuning sometimes accompanies alignment in complex formulas. The combination of alignment and custom spacing creates clean delineated structure. This further boosts the readability payoff provided by display environments.
Note however that intricate alignment risks crowding symbols together and introduces whitespace. Judicious stopping points on alignment complexity prevent clutter that ultimately decreases comprehensibility.
Example Alignments
-
\begin{align*}
f(x) &= ax^2 + bx + c\\
g(x) &= dx^3 + ex^2 + fx + g
\end{align*} -
\begin{aligned}
S &= \{s \in \mathbb{R} \mid s \geq 0\}\\
T &= \{t \in \mathbb{R} \mid t < 0\} \end{aligned}
Inserting Text in Math Mode
Inline textual annotations guide interpretation of mathematical symbols. LaTeX provides \text{...} and \textrm{...} for embedding word fragments into math expressions when needed.
Sparse thoughtful text insertion contributes significantly to the self-documenting quality of equations. But dense usage risks visual clutter undermining the fluency benefits of notation.
Display math generally warrants more textual mix-ins than inline formulas. Verbose mixed text and math styling is incompatible with the flow constraints of paragraph embedding.
Example Text Insertions
- Set membership: $x \in \mathbb{R}_{\textrm{odd}}$
- Inline definition: velocity $\mathbf{v} = \text{d}\mathbf{s}/\text{d}t$
- Multiplication:
\begin{equation*}
\text{Force} = \text{mass} \times \text{acceleration}
\end{equation*}
Using Math Packages for Advanced Typesetting
A suite of dedicated math packages unlock sophisticated typesetting capabilities. Notably, the comprehensive amsmath package provides advanced math environments, macros and symbols.
For example, amsmath adds cases constructs via \begin{cases} for piecewise definitions with automatic alignment across cases. Many new operator and arrow commands like \propto also derive from amsmath.
Packages like mathtools, nccmath, physics and mhchem provide still more domain-specific math extensions. Tapping into these tools yields semantic typesetting payoff beyond basic LaTeX.
However math packages introduce coding overhead and reliance on external tooling. The return on added complexity must justify cost to maintain readability and authoring flow.
Example Package-Based Typesetting
-
Piecewise function:
\begin{cases}
x, & \text{if } x \geq 0 \\
-x, & \text{if } x < 0 \end{cases} -
Physics equation with \propto operator:
$F \propto {\dot{p}}$
Examples of Beautiful and Readable Math Expressions
The deepest insights emerge from equations melding mathematical depth with lucid syntax. The following samples showcase LaTeX typesetting prowess in distilling complex concepts into compelling symbolic representations.
The Cauchy-Schwarz Inequality
The Cauchy-Schwarz inequality sets fundamental boundaries on inner products in vector spaces. LaTeX deftly handles the algebra complexity while showing parallel structure through alignment.
The Log-Sum-Exp Technique
The log-sum-exp method numerically stabilizes summation of exponentiated values. LaTeX align environments cleanly arrange the equation flow across lines.
These examples showcase aesthetically striking yet easily parsed math. LaTeX empowers authors to render communicate demanding mathematical ideas this effectively.
Common Issues and How to Fix Them
Fluent math typesetting involves avoiding common math rendering issues. Learning to navigate these pitfalls helps authors produce consistently polished formulas.
Cluttered Expressions
Dense equations without visual structure strain cognitive parsing. LaTeX environments like {multline} and {aligned} tidy lengthy expressions through line breaks and alignment while still treating them as a unit.
Imbalanced Spacing
Isolated spacing problems stem from missing glue and gaps between symbols. Manual spacing tuning with inter-math padding \; and post-formula whitespace \quad restores balance.
Pixelated Symbols
Formula symbols rendering badly at small font sizes owes to underlying rasterized fonts. Enabling outline math fonts via \usefonttheme{professionalfonts} sharpens up zoomed-out math.
Overflowing Margins
Page layout errors with equations crossing margins usually indicates display math sizing issues. Manual overrides using {small}, {Large} or even {resizebox} constrain oversized renderings.
Finding the Right Balance Between Aesthetics and Clarity
This exploration of core math typesetting components in LaTeX demonstrates the coupling between attractive presentation and intelligible structure. While seemingly at odds mathematically beautiful expressions rely intrinsically on lucid readable foundations.
Harmony emerges only through intentional balancing of aesthetic and functional concerns both macroscopically across the whole document and at focused local scales. Beautiful math communication requires this synthesis of form and function.
LaTeX offers unmatched capabilities for finely controlling math typesetting. Yielding its tools with readability as the guiding focus enables technical authors to serve the mathematical depth underpinning science and engineering discoveries.
