Pi Is (still) Wrong. Golden Ratio. The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron.
It is denoted , or sometimes The designations "phi" (for the golden ratio conjugate ) and "Phi" (for the larger quantity ) are sometimes also used (Knott), although this usage is not necessarily recommended. Fibonacci Sequence (PRIME) Medieval mathematician and businessman Fibonacci (Leonardo of Pisa) posed the following problem in his treatise Liber Abaci (pub. 1202): How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?
It is easy to see that 1 pair will be produced the first month, and 1 pair also in the second month (since the new pair produced in the first month is not yet mature), and in the third month 2 pairs will be produced, one by the original pair and one by the pair which was produced in the first month. In the fourth month 3 pairs will be produced, and in the fifth month 5 pairs. After this things expand rapidly, and we get the following sequence of numbers: 1,1,2,3,5,8,13,21,34,55,89,\ldots.