# Pascal triangle

$$\begin{array}{c} {} \\ {} \\ {} \\ {} \\ {} \\ {} \\ 1 \end{array} \ \begin{array}{c} {} \\ {} \\ {} \\ {} \\ {} \\ 1 \\ \cdot \end{array} \ \begin{array}{c} {} \\ {} \\ {} \\ {} \\ 1 \\ {} \\ \cdot \end{array} \ \begin{array}{c} {} \\ {} \\ {} \\ 1 \\ {} \\ 5 \\ \cdot \end{array} \ \begin{array}{c} {} \\ {} \\ 1 \\ {} \\ 4 \\ {} \\ \cdot \end{array} \ \begin{array}{c} {} \\ 1 \\ {} \\ 3 \\ {} \\ 10 \\ \cdot \end{array} \ \begin{array}{c} 1 \\ {} \\ 2 \\ {} \\ 6 \\ {} \\ \cdot \end{array} \ \begin{array}{c} {} \\ 1 \\ {} \\ 3 \\ {} \\ 10 \\ \cdot \end{array} \ \begin{array}{c} {} \\ {} \\ 1 \\ {} \\ 4 \\ {} \\ \cdot \end{array} \ \begin{array}{c} {} \\ {} \\ {} \\ 1 \\ {} \\ 5 \\ \cdot \end{array} \ \begin{array}{c} {} \\ {} \\ {} \\ {} \\ 1 \\ {} \\ \cdot \end{array} \ \begin{array}{c} {} \\ {} \\ {} \\ {} \\ {} \\ 1 \\ \cdot \end{array} \ \begin{array}{c} {} \\ {} \\ {} \\ {} \\ {} \\ {} \\ 1 \end{array}$$
In the row numbered $n+ 1$ there appear the coefficients of the expansion of the binomial $( a+ b) ^ {n}$. The triangular table presented by B. Pascal in his Treatise on an arithmetical triangle (1654) differs from the one described above by a rotation through $45\circ$. Tables for the representation of the binomial coefficients were known even earlier.