The golden ratio, represented by the Greek letter, φ (phi), is equal to (sqrt(5)+1)/2. This number makes a very interesting base because of this special property: φ2 = φ + 1, which means 100φ = 011φ and 0200φ = 1001φ. These two rules can be applied in either direction against any sequence of consecutive digits in a base-φ number to put it in "standard form", which means no digits other than 0 or 1, and no two 1's in a row. In addition, the repeating decimal 0.101010... is equal to 1. 100φ = 011φ This relation can be applied anywhere in a base-φ number to handle most "carries" when adding. So, for example, 111.111 +111.111 -------- 222.222 is the result after doing the addition, but the "2" digits in the result aren't considered "normal form", so they must be reorganized into zeros and ones by "carrying" the digits to the left. Unlike integer base arithmetic, in which digits need to be carried only ...