\documentclass{article}

\begin{document}
If $a,b,c$ are the sides of a right triangle and $c$ is the hypotenuse, then
\begin{equation}
a^2 + b^2 = c^2.
\end{equation}

\begin{equation}
\varphi = \frac{1 + \sqrt{5}}{2}
\end{equation}

\begin{equation}
e^{i\pi} - 1 = 0
\end{equation}

\begin{equation}
f'(t) = \lim_{h \rightarrow 0} \frac{f(t + h) - f(t)}{h}
\end{equation}

\begin{equation}
F = G\frac{m_1m_2}{d^2}
\end{equation}


\begin{equation}
F(f)(\zeta) = \int_{-\infty}^\infty f(x) e^{-2\pi i x \zeta}dx
\end{equation}

If $a_0 = 0$ and $a_1 = 1$, then
\begin{equation}
a_{n+2} = a_{n+1} + a_n 
\end{equation}

\begin{equation}
\int_a^b f'(x)dx = f(b) - f(a)
\end{equation}

\begin{equation}
\clubsuit \diamondsuit \heartsuit \spadesuit
\end{equation}


\end{document}
