This made it click for me. Thanks for explaining. Just to expand a bit on the vertex thing, in 2 dimensions length is sqrt(x^2 + y^2). For a square of side len

This made it click for me. Thanks for explaining. Just to expand a bit on the vertex thing, in 2 dimensions length is sqrt(x^2 + y^2). For a square of side length 2 the distance from the center to each vertex is sqrt(1^2 + 1^2) or sqrt(2 * 1). For 3 dimensions it's sqrt(x^2 + y^2 + z^2) or sqrt(3 * 1). For one million dimensions the distance to each vertex is sqrt(1,000,000) or 1,000 while the distance to each side is still 1.