The Fibonacci sequence is also known as the Fibonacci spiral or the Fibonacci numbers. The most common reference of this sequence is the Fibonacci tiling, which are blocks with the sizing of each number. This can be seen in the photos above. This is a sequence of numbers that either always begins with 1 and 1 or  0 and 1 depending on the starting point of the sequence, the subsequent number is the sum of the previous two (e.g. 1, 1 = 2, 5, 8 = 13). The beginning of the sequence looks like this: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... etc. An example of this can be seen in the photos above. The Fibonacci spiral is an approximation of the golden spiral which is created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling.

 

Mathematics

The sequence is defined by the recurrence relation: Fn = Fn-1 + Fn-2 with seed values F1 = 1, F2 = 1 or F1 = 0, F1 = 1.

 

Fibonacci numbers are closely related to Lucas numbers 'Ln' in that they form a complementary pair of Lucas sequences Un(1,-1) = Fn and Vn (1,-1) = Ln. They are intimately connected with the golden ratio; for example, the closest rational approximations to the ratio are 2/1, 3/2, 5/3, 8/5...etc.

 

Biology

Fibonacci numbers are often seen in biological setting such as the growth of tree branches, phyllotaxis (the arrangement of leaves on a stem), in the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone bract's.

 

The Inventor

The Fibonacci sequence was invented by an Italian man by the name of Leonardo of Pisa, also known as Fibonacci. Fibonacci published a book in 1202 called "Liber Abaci" which introduced the sequence into Western European mathematics. The sequence was originally in Indian mathematics and was called 'Virahanka', named after an Indian prododist who was known for his work in mathematics.