Let a < b be real numbers. The Cartesian product [a, b] [a, b] is obviously

Question:

Let a < b be real numbers. The Cartesian product [a, b] × [a, b] is obviously a square in R2. Define a cube Q in R" to be the n-fold Cartesian product of [a, b] with itself; that is, Q := [a, b] × ∙ ∙ ∙ × [a, b]. Find a formula of the angle between the longest diagonal of Q and any of its edges. Show that when n = 3, this angle is approximately 54.74 degrees.