Mathematical Formulas

TreeMk supports rendering mathematical formulas using LaTeX syntax powered by KaTeX. You can write both inline and display (block) formulas.

Inline Formulas

For inline formulas within text, wrap your LaTeX code with single dollar signs $...$:

Example:

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ where $a \neq 0$.

Renders as:
The quadratic formula is \(x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\) where \(a \neq 0\).

Display Formulas

For display formulas that appear on their own line, use double dollar signs $$...$$:

Example:

$$
E = mc^2
$$

Renders as:

\[ E = mc^2 \]

Common Mathematical Notation

Fractions and Roots

$$
\frac{1}{2} \quad \frac{a}{b+c} \quad \sqrt{x} \quad \sqrt[3]{x}
$$

\[ \frac{1}{2} \quad \frac{a}{b+c} \quad \sqrt{x} \quad \sqrt[3]{x} \]

Superscripts and Subscripts

$$
x^2 \quad x^{10} \quad x_i \quad x_{ij} \quad x_i^2
$$

\[ x^2 \quad x^{10} \quad x_i \quad x_{ij} \quad x_i^2 \]

Greek Letters

$$
\alpha, \beta, \gamma, \Delta, \Theta, \pi, \omega, \Omega
$$

\[ \alpha, \beta, \gamma, \Delta, \Theta, \pi, \omega, \Omega \]

Summation and Integration

$$
\sum_{i=1}^{n} x_i \quad \int_{0}^{\infty} e^{-x} dx
$$

\[ \sum_{i=1}^{n} x_i \quad \int_{0}^{\infty} e^{-x} dx \]

Matrices

$$
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
\quad
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6
\end{bmatrix}
$$

\[ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \quad \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \]

Advanced Examples

Calculus

The derivative of a function:

$$
f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
$$

\[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \]

Linear Algebra

System of equations:

$$
\begin{cases}
2x + 3y = 5 \\
x - y = 1
\end{cases}
$$

\[ \begin{cases} 2x + 3y = 5 \\ x - y = 1 \end{cases} \]

Statistics

Normal distribution probability density function:

$$
f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}
$$

\[ f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2} \]

Tips

• Preview - Use the preview pane to see your formulas rendered in real-time
• Escaping - To show a literal dollar sign, use \$
• Alignment - Use \quad for spacing or \begin{aligned}...\end{aligned} for multi-line alignment
• Reference - For complete LaTeX syntax, see the KaTeX documentation

Troubleshooting

Formula not rendering? - Check for matching dollar signs - Ensure LaTeX syntax is correct - Look for unescaped special characters

Common LaTeX commands: - \frac{numerator}{denominator} - fractions - \sqrt{x} - square root - ^ - superscript - _ - subscript - \left( ... \right) - auto-sized parentheses - \text{...} - regular text inside formulas