Say you have three (distinct) points on the unit sphere in Euclidean space $$p_1, p_2, p_3 \in S^n = \{ x \in \mathbb R^{n+1} : |x| = 1 \}$$ I'd like to find, as efficiently and robustly as possible, a description of the unique round circle in $S^n$ that contains the three points. By round cir...

Let $X$ be a normed space and $Y$ a closed subspace of $X$ and $Y^0=\{f \in X^*|f(x)=0,\forall y \in Y\}$. Prove that $Y^0$ is isometricaly isomorphic with $(X/Y)^*$. I have to find a function specifically between $Y^0 $ and $(X/Y)^*$. One idea is the function $S: Y^0 \longrightarrow (X/Y)^*$...