1170, Pisa? —died after 1240), medieval Italian mathematician who wrote Liber abaci (1202; “Book of the Abacus”), the first European work on Indian and Arabian mathematics, which introduced Hindu-Arabic numerals to Europe.

In this series, each number is the sum of the two preceding numbers. For example, 3 = 1 + 2, and 5 = 3 + 2. Therefore, the number following 13 must be 13 + 8 = 21, and the next number must be 21 + 13 = 34.

The first 12 terms of the Fibonacci sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The 12th term (144) gives the number of rabbits after one year, which answers Fibonacci’s original question to his readers.

Pisa

Leonardo Fibonacci, also known as Leonardo of Pisa or Leonardo Pisano was born sometime around 1175 in Pisa, Italy into the Bonacci family. You many Pisa from its associated Leaning Tower of Pisa, whose earliest construction started right around the time of Fibonacci’s birth.

Throughout history, the ratio for length to width of rectangles of 1.61803 39887 49894 84820 has been considered the most pleasing to the eye. This ratio was named the golden ratio by the Greeks. In the world of mathematics, the numeric value is called “phi”, named for the Greek sculptor Phidias.

For example, the measurement from the navel to the floor and the top of the head to the navel is the golden ratio. Animal bodies exhibit similar tendencies, including dolphins (the eye, fins and tail all fall at Golden Sections), starfish, sand dollars, sea urchins, ants, and honey bees.

The Fibonacci Studies and Finance When used in technical analysis, the golden ratio is typically translated into three percentages: 38.2%, 50%, and 61.8%. However, more multiples can be used when needed, such as 23.6%, 161.8%, 423%, and so on.