MODULE 1.1

• The Fibonacci sequence is a mathematical sequence that begins with one and each subsequent number is the sum of the two preceding numbers, represented by the equation Fib(n) = Fib(n - 1) + Fib(n - 2).
• The Fibonacci sequence begins as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144……………….
• Fibonacci applied the Fibonacci sequence to a problem involving the breeding of rabbits, mapping the family tree of a group of rabbits that initially started with only two members.
• The number of rabbits at any given time was always in the Fibonacci number.
• The Fibonacci sequence has numerous naturally occurring applications, ranging from the very basic to the complex geometric shapes.
• The number of petals on a flower tend to be a Fibonacci number.
• Branching plants always branch off into groups of Fibonacci numbers.
• Leaf Orientation also exhibits Fibonacci numbers.
• You have 5 fingers on each hand, 5 toes on each foot, 2 arms, 2 legs, 2 eyes, 2 ears, 1 nose with 2 nostrils, which are all on the Fibonacci Sequence.
• Both the Fibonacci sequence and the golden ratio are used to guide design for architecture, websites, and many more.
• A spiral can then be drawn starting from the corner of the first rectangle of side length 1, all the way to the corner of the rectangle of side length 13.
• The Fibonacci spiral is constructed by placing together rectangles of relative side lengths equaling Fibonacci numbers.
• The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by one, and proceeds based on the rule that each number (Fibonacci number) is equal to the sum of the preceding two numbers.
• The ratio between two numbers in the Fibonacci sequence eventually approaches the “Golden ratio” as a limit.
• The Fibonacci sequence is related to the golden ration, a proportion (1:1.618) that occurs frequently throughout the natural world and is applied across many areas of human endeavor.
• Mathematically, Phi (Φ) is equal to 1 + √ " # or Approximately 1.618034.
• Fibonacci numbers have geometric application in nature as well.
• Phi (Φ) is defined as the limit of the ratio of a Fibonacci number n and its predecessor, Fib (n - 1).
• Mathematician refer to a number known as Phi (Φ) as a significant application of the Fibonacci sequence.