# Methane In $$\mathbb{R}^4$$?

Geometry Level 5

Consider five nonzero vectors in $$\mathbb{R}^4$$ such that any two of them enclose the same nonzero angle $$\theta$$. Find $$\cos\theta$$, to two significant digits.

Bonus Question: Find the corresponding angle $$\theta_n$$ between $$n+1$$ nonzero vectors in $$\mathbb{R^n}$$ and find $$\displaystyle \lim_{n\to\infty}\theta_n$$.

Note that $$\theta_3$$ is the bond angle in the methane molecule.

×