Fibonacci series and Golden ratio
- 1. FIBONACCI SERIES AND THE GOLDEN RATIO SYNDICATE # 04
- 2. WHAT IS THE GOLDEN RATIO? LET US CLEAR WITH AN EXAMPLE, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 CONSIDER THE SERIES TO GET THE NEXT NUMBER WE ADD THE PREVIOUS TWO NUMBERS TOGETHER. SO NOW OUR SEQUENCE BECOMES 1, 1, 2. THE NEXT NUMBER WILL BE 3.
- 3. Now, I know what you might be thinking: "What does this have to do with the Golden Ratio? This sequence of numbers was first “discovered” by a man named Leonardo Fibonacci, and hence is known as Fibonacci's sequence.
- 4. SERIES RATIO SERIES RATIO 2 2 55 1.617647059 3 1.5 89 1.618181818 5 1.666666666 144 1.617977528 8 1.6 233 1.618055555 13 1.625 377 1.618025751 21 1.615384615 610 1.618037135 34 1.619047619 987 1.618032787
- 5. CONCLUSION FROM TABLE The Golden Ratio is what we call an irrational number: it has an infinite number of decimal places and it never repeats itself! Generally, we round the Golden Ratio to 1.618.
- 6. VALUE OF PHI (AN IRRATIONAL NUMBER) ∅ = 1+ 5 2
- 7. NTH TERM OF FIBONACCI SERIES
- 8. IN TERMS OF PHI
- 9. GENERAL TERM OF FIBONACCI SERIES
- 11. The Proportions in the Body The white line is the body's height. The blue line, a golden section of the white line, defines the distance from the head to the finger tips The yellow line, a golden section of the blue line, defines the distance from the head to the navel and the elbows. The green line, a golden section of the yellow line, defines the distance from the head to the pectorals and inside top of the arms, the width of the shoulders, the length of the forearm and the shin bone. The magenta line, a golden section of the green line, defines the distance from the head to the base of the skull and the width of the abdomen. The sectioned portions of the magenta line determine the position of the nose and the hairline. Although not shown, the golden section of the magenta line (also the short section of the green line) defines the width of the head and half the width of the chest and the hips.
- 13. The ratio of your forearm to hand is Phi
- 14. Your hand shows Phi and the Fibonacci Series Your Index Finger
- 16. METHOD ONE 1. WE'LL START BY MAKING A SQUARE, ANY SQUARE LIKE THIS
- 17. 2. NOW, LET'S DIVIDE THE SQUARE IN HALF (BISECT IT). BE SURE TO USE YOUR PROTRACTOR TO DIVIDE THE BASE AND TO FORM ANOTHER 90 DEGREE ANGLE.
- 18. 3. NOW, DRAW IN ONE OF THE DIAGONALS OF ONE OF THE RECTANGLES
- 19. 4. MEASURE THE LENGTH OF THE DIAGONAL AND MAKE A NOTE OF IT.
- 20. 5. NOW EXTEND THE BASE OF THE SQUARE FROM THE MIDPOINT OF THE BASE BY A DISTANCE EQUAL TO THE LENGTH OF THE DIAGONAL
- 21. 6. CONSTRUCT A NEW LINE PERPENDICULAR TO THE BASE AT THE END OF OUR NEW LINE, AND THEN CONNECT TO FORM A RECTANGLE
- 22. 7. MEASURE THE LENGTH AND THE WIDTH OF YOUR RECTANGLE. NOW, FIND THE RATIO OF THE LENGTH TO THE WIDTH. ARE YOU SURPRISED BY THE RESULT? THE RECTANGLE YOU HAVE MADE IS CALLED A GOLDEN RECTANGLE BECAUSE IT IS "PERFECTLY" PROPORTIONAL.
- 26. FIBONACCI SEQUENCE IN VEGETABLES