Fibonacci series

Sequence of numbers in which 1 appears twice as the first two numbers, and every subsequent number is the sum of two preceding numbers: 1, 1, 2, 3, 5, 8, 13 ... and so on. As it continues, the ratio between any number and its successor approaches the ratio of golden section (1:1.618). Discovered around 1202 by the Italian mathematician Fibonacci (circa 1175-1250), it displays unique mathematical properties that make it useful in fields as diverse as astronomy (distances between planets and the sun, and the shape of galactic spirals), botany (growth patterns of plants and trees), and financial markets (price movements of securities).