Maths and Code

Inline maths like $e^{i\pi} + 1 = 0$ and display maths:

$$ \int_0^1 x^2 \, dx = \frac{1}{3} $$

Long formulas stay inside the column on phones. In a sentence, the composite trapezoidal rule $\int_a^b f(x)\,dx \approx \frac{h}{2}\left(f(x_0) + 2f(x_1) + 2f(x_2) + \dots + 2f(x_{n-1}) + f(x_n)\right)$ breaks across lines like words do; on its own line, a formula too wide to break scrolls sideways:

$$ \left\lVert u - u_h \right\rVert_{L^2(\Omega)} \le C h^{p+1} \left\lvert u \right\rvert_{H^{p+1}(\Omega)} \quad\text{for all}\quad u \in H^{p+1}(\Omega) \cap H^1_0(\Omega),\ h \to 0 $$

Code gets the theme’s colours in light and dark mode:

def trapezoid(f, a, b, n):
    h = (b - a) / n
    return h * (f(a) / 2 + sum(f(a + i * h) for i in range(1, n)) + f(b) / 2)

A quote, for good measure.