P3

• Fibonacci sequence


  A series of numbers where a number is found by adding up the two numbers before it.

  
• Fibonacci sequence


  The sequence of numbers, starting with zero and one, is a steadily increasing series where each number is equal to the sum of the preceding two numbers.

  
• Fibonacci


  Also known as Leonardo of Pisa or Leonardo Pisano
• Fibonacci, an Italian mathematician, developed the Fibonacci sequence


  13th century
• Fibonacci numbers were first introduced in his Liber Abbaci (Book of Calculation)


  1202
• Fibonacci sequence rule or Recursive Formula

  xn = xn−1 + xn−2, where xn is term number "n", xn−1 is the previous term (n−1), and xn−2 is the term before that (n−2)
• Golden ratio


  The relationship between numbers on the Fibonacci sequence where plotting the relationships on scales results in a spiral shape
• Golden ratio


  Derived by dividing each number of the Fibonacci series by its immediate predecessor
• The golden ratio was first called the Divine Proportion


  Early 1500s
• Luca Pacioli's work "De Divina Proportione" explored the golden ratio


  1509
• Golden ratio


  Approximately equal to 1.618034, used to calculate the Fibonacci number, denoted by the Greek letter "phi" 𝜑 𝑜𝑟 𝜙
• Binet's formula


  An equation which gives the nth Fibonacci number as a difference of positive and negative nth powers of the golden ratio

  Fn = (1 + square root of 5 / 2)^n - (1 - square root of 5 / 2)^n / square root of 5
• Fibonacci spiral


  The limits of the squares of successive Fibonacci numbers create a spiral known as the Fibonacci spiral, following turns by a constant angle close to the golden ratio, commonly called the golden spiral