Fibonacci and golden ratio
- 1. Fibonacci Sequence and Golden Ratio -Aditya Garg 11-C Vasant Valley School
- 2. Contents Fibonacci sequence How does Fibonacci sequence work Golden Ratio Applications of Golden Ratio Some interesting facts
- 3. Fibonacci sequence It is series of numbers that follow a unique integer sequence. Inventedby Leonardo Fibonacci. It is closely related to Lucas numbers and Golden Ratio. The Fibonacci numbers are 1,1,2,3,5,8,13,etc.
- 4. How does the Fibonacci sequence work The numbers of the series are obtained by adding the two previous numbers in the sequence to obtain the next higher number. Example: 1+1=2,1+2=3,3+2=5,5+8=13,etc. Formulais: An=An-1+An-2 for n>=3 where : An is term number "n“ An-1 is the previous term (n-1) An-2 is the term before that (n-2) A1=A2=1 When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the GOLDEN RATIO (1.618034).
- 5. Golden Ratio The golden ratio (symbol is the Greek letter "phi(φ)) is a special number approximately equal to 1.618 It can also be calculates as 2 x Sin (54 degree) It appears many times in geometry, art, architecture and other areas. The ratio of each successive pair of numbers in the Fibonacci Sequence converge on the golden ratio as we go higher in the sequence. 3/2 = 1.5 5/3 = 1.66666666666666… 8/5 = 1.6 3/8 = 1.625 21/13 = 1.61538461538462… 34/21 = 1.61904761904762… 55/34 = 1.61764705882353… 89/55 = 1.61818181818182…
- 6. Applications Of Golden Ratio Architecture Painting Book Design Nature Aesthetics Perceptual Studies
- 7. Do you know? Fibonacci numbers frequently appear in the numbers of petals in a flower and in the spirals of plants. The positions and proportions of the key dimensions of many animals are based on Phi(φ). The diameters of the Earth and Moon form a triangle whose dimensions are based on the mathematical characteristics of phi. The distances of the planets from the sun correlate surprisingly closelyto exponential powers of Phi(φ). Golden Ratio is used in the design of the Apple logo!!!
- 8. Golden Ratio is Everywhere!!!
- 9. Fibonacci Day? NOVEMBER 23. WHY? 11/23 1 1 2 3
- 10. THANK YOU