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The fibonacci sequence
- 2. What is fibonacci sequence? • Fibonacci sequence is a series of numbers that follow a unique integer sequence. • These numbers generate mathematical patterns that can be found in all aspects of life. • The patterns can be seen in everything from the human body to the physiology of plants and animals. • The fibonacci sequence is derived from the fibonacci numbers.
- 3. How are these fibonacci numbers obtained? • These numbers are obtained from the formula- Fn=Fn-1+Fn-2 • These numbers are obtained by adding the two previous numbers in the sequence to obtain the next higher number.
- 4. HOW DOES THE FIBONACCI SEQUENCE WORK? • The Fibonacci sequence is as follows: 0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610..and so on. • As a rule the first 2 numbers in the sequence has to be 0 and 1 .All other numbers follow the rule of adding the two previous numbers in the sequence. EXAMPLE: 1+1=2, 2+3=5, 5+3=8 • Every third number in the sequence is even.
- 5. What is the history of the fibonacci sequence? • The exact date of origin of the Fibonacci sequence is unknown. • It is believed that contributions to the theory began in 200 BC by Indian mathematicians whose studies were based in the language of Sanskrit. • The sequence was introduced to Western European mathematicians in 1202 by Aka Fibonacci (famous as the Leonardo of Pisa).
- 6. • His study of the sequence began with the breeding patterns of rabbits. In which, he found rabbit generations duplicated in accordance with the Fibonacci numbers.
- 7. Fibonacci rectangle • The Fibonacci rectangle is a rectangle which is further divided into squares whose lengths are the consecutive numbers of the Fibonacci sequence.
- 8. Fibonacci spiral • This spiral is created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci rectangle. • The numbers form what are called as Fibonacci rectangles. These rectangles are unique because each rectangle has length of sides equal to the magnitude of the Fibonacci numbers. • Within these rectangles we can create a spiral with cross sections equal to exactly 1.618 (the golden mean) with the corresponding angle of 137.5 degrees.
- 10. Fibonacci sequence in petal patterns • The Fibonacci sequence can be seen in most petal patterns. For example, most daisies have 34,55or 89 petals and most common flowers have 5, 8 or 13 petals.
- 11. Fibonacci sequence in sunflowers • The Fibonacci sequence can be found in a sunflower heads seed arrangement . • The arrangement of seeds corresponds to Fibonacci spiral and they are arranged in an angle of 137.5 degrees which is also called the ‘golden angle’.
- 12. Fibonacci sequence in pine cones
- 13. Fibonacci sequence in sea shells • The Fibonacci spiral directly correspond to the spiral found in sea shells.
- 14. Fibonacci is also found in monalisa TOO!
- 15. FIBONACCI SEQUENCE IN HUMAN BODY
- 16. THANK YOU -SMRUTI S SHETTY XC , G17 Sharada Vidyalaya, Mangalore