Fibonacci Sequence

• The sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, … is called the Fibonacci sequence and its terms the Fibonacci numbers. 
• The Fibonacci sequence is the sequence f1, f2, f3, f4, … which has its first two terms f1 and f2 both equal to 1 and satisfies thereafter the recursion formula fn = fn–1 + fn–2. 
• A golden rectangle can be broken into squares the size of the next Fibonacci number down and below. 
• Fibonacci spiral – 

  Take a golden rectangle, break it down into smaller squares based from Fibonacci sequence and divide each with an arc.
• Luca Pacioli found the relationship between Fibonacci sequence and the golden ratio. 
• The golden ratio was first called as the Divine Proportion in the early 1500s in Leonardo da Vinci’s work was explored by Luca Pacioli (Italian mathematician) entitled “De Devina Proportione” in 1509. 
• Two quantities are in the Golden ratio if their ratio is the same of their sum to the larger of the two quantities. 
• The Golden Ratio is the relationship between numbers on the Fibonacci sequence where plotting the relationships on scales results in a spiral shape
• Golden Ratio is approximately 1.61803398875.
• Golden Spirals - A curve that grows at a constant rate while spiraling around a fixed point. It has been observed in nature such as nautilus shells, sunflowers, pinecones, etc.
• Symmetry is a sense of harmonious and beautiful proportion of balance or if an object is invariant to any of various transformations (reflection, rotation or scaling). 
• Radial symmetry (or rotational symmetry) is a type of symmetry around a fixed point known as the center and it can be classified as either cyclic or dihedral. 

  
• Bilateral or reflection symmetry is the simplest kind of symmetry. It is one of the most common kinds of symmetry that we see in the natural world. It can also be called mirror symmetry because an object with this symmetry looks unchanged if a mirror passes through its middle. In other words, the objects have a left side and a right side that are mirror images of each other.