Abstract

Let $C\subset \PP n$ be a rational normal curve and let $\ell_O:\PP {n+1}\dashrightarrow \PP n$ be any tangential projection form a point $O\in T_AC$ where $A\in C$. In this paper we relate the minimum number $r$ of addenda that are needed to write a binary form $p$ of degree $(n+1)$ and defined over an algebraically closed field of characteristic zero as linear combination of $(n+1)$-th powers of linear binary forms $L_1, \ldots , L_r$, with the minimum number of addenda that are required to write $\ell_O(p)$ as linear combination of elements belonging to $\ell_O(C)$.