Definition: The normed B-Splines $N_k^m$ of degree $m\geq 1$ are recursively defined as
$\hspace{4,5cm}N_k^0(x)=\begin{cases} 1, & \text{if}\ x\in[x_k,x_{k+1}) \\ 0, & \text{else} \end{cases}$
and
$\hspace{2cm} N^m_k(x)=\dfrac{x-x_k}{x_{k+m}-x_k}N^{m-1}_k(x)+\dfrac{x_{k+m+1}-x}{x_{k+m+1}-x_{k+1}}N_{k+1}^{m-1}(x)$
where the $x_i$ are the spline knots in and around $[a,b]\in\mathbb{R}$ on which we wish to define our splines. The knots around $[a,b]$ where introduced to prevent having to do case distinctions at the edges for our normed B-Splines.
Now I'm able to work with this definition, but I would be interested in learning more about the intuition behind it and how people actually came up with this rather big formula and why we have to "norm" them.