Cube root polar angle by three in order to define a cube root. With this definition, the principal cube root of a negative number is a complex number, and for instance will not be −2, but rather . This difficulty can also be solved by considering the cube root as a multivalued function: if we write the original complex number "x" in three equivalent forms, namely The principal complex cube roots of these three forms are then respectively Unless , these three complex numbers are distinct, even though the three representations of "x" were equivalent. For example, may then be calculated to
Partial cube root vertex "r" for the tree, arbitrarily, and label each vertex "v" with a string of "m" bits that has a 1 in position "i" whenever edge "i" lies on the path from "r" to "v" in "T". For instance, "r" itself will have a label that is all zero bits, its neighbors will have labels with a single 1-bit, etc. Then the Hamming distance between any two labels is the distance between the two vertices in the tree, so this labeling shows that "T" is a partial cube. Every hypercube graph is itself a partial cube, which can be