Shapey Numbers

$\newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}}$

We all know about numbers that form squares, we often call them square numbers.

For any natural number $n$, the $n$^th^ square number is $n^2$.

For the uninitiated, $n^2 = \int_{0}^{n} \frac{x}{2} dx$

Triangle numbers

These are numbers that can be arranged into triangles. This is also the sum of the first $n$ consecutive natural numbers.

$\sum_{i = 1}^{n} i = \frac{n(n - 1)}{2}$

Also, $1.5 \in \R$