Pythagorean theorem

Pythagorean theorem: if $\triangle ABC$ is right at $A$ then:

$AB^2 + AC^2 = BC^2$

Area of a circle:

$\begin{aligned} \mathrm{Area}(r) &{}= \iint_D 1\ d(x, y)\\ &{} = \iint_D t\ dt\ d\theta\\ &{} = \int_0^r \int_0^{2\pi} t\ d\theta\ dt\\ &{} = \int_0^r \left[ t\theta \right]_{0}^{2\pi} dt\\ &{}= \int_0^{r} 2 \pi t \, dt \\ \end{aligned}$