begin{defn} An emph{affine combination} of points $x_1, x_2, ldots, x_k$ is given by $sumlimits_{i=1}^k lambda_{i}x_{i}$, where $lambda_1,ldots, lambda_k  in mathbb{R}$ and $sumlimits_{i=1}^k lambda_{i} = 1$. A set of points is said to be emph{affinely independent} if no point is an affine combination of the others.
end{defn}