English: Illustrates the Cauchy-Schwarz inequality ${\displaystyle |\langle x,y\rangle |^{2}\leqslant \langle x,x\rangle \cdot \langle y,y\rangle }$ for the special case of two unit-length vectors ${\displaystyle x}$ and ${\displaystyle y}$ in the Euclidean plane: Since ${\displaystyle \langle x,x\rangle =1=\langle y,y\rangle }$, and ${\displaystyle \langle x,y\rangle =\cos(\varphi )}$, the inequality boils down to the well known ${\displaystyle \cos(\varphi )^{2}\leqslant 1}$.