1. So the volume of the unit cube is 1 as expected. 2. Show a point moving inside a solid unit cube . 3. In other words, it is topologically indistinguishable from the unit cube of countably infinite dimension. 4. The Gaussian copula is a distribution over the unit cube [ 0, 1 ] ^ d. 5. Another way to express the same problem is to ask for the largest square that lies within a unit cube . 6. More generally, show how to find the largest rectangle of a given aspect ratio that lies within a unit cube . 7. Each unit cube contains a cubic unit of volume and each of the surfaces of the cubes are a square unit of area. 8. Then there is a point in the-dimensional unit cube in which all functions are " simultaneously " equal to. 9. :I gather you want to write an arbitrary point in the interior of the unit cube as a convex combination of the eight vertices. 10. In algebraic terms, doubling a unit cube requires the construction of a line segment of length, where; in other words, } }.