![FIBONACCI SEQUENCE IN A SEASHELL
THE FIBONACCI NUMBERS DIRECTLY CORRESPONDS TO THE
SPIRALS FOUND IN A SUBSHELLS .
THE NUMBERS FORM WHAT WE CALLED FIBONACCI RECTANGLES
OR “GOLDEN RECTANGLES”.
THE RECTANGLES ARE UNIQUE BECAUSE EACH RECTANGLES HAS
SIDE EQUAL TO THE LENGTH OF FIBONACCI NUMBERS.
WITHIN THESE RECTANGLES WE CAN CREATE A SPIRAL WITH
CROSS SECTIONS EQUAL TO THE EXACTLY 1.618[“GOLDEN MEAN”
WITH THE CROSSEPONDING ANGLE OF 137.5°.]](https://image.slidesharecdn.com/fibonaccisequencemathsexb-1-241207050117-d43cad7c/85/FIBONACCI-SEQUENCE-MATHS-Exb-1-pptxiiiii-8-320.jpg)
FIBONACCI SEQUENCE MATHS Exb-1.pptxiiiii
- 1. FIBONACCI SEQUENCE It’s nothing but 0 ,1 ,1 ,2 ,3 ,5,8,13,21……….. IN ORDER TO UNDERSTAND WHAT IS FIBONACCI SEQUENCE . LET’S FIRST SEE THE DEFINATION OF A SEQUENCE …….. SEQUENCE – Sequence refers to the enumerated collection of objects in which repetition is allowed and order matters . EXAMPLE – (i) 2,3,5,7,9,11,……. (ii) 3,6,12,24,48,……
- 2. Types of Sequences Following are the types of the sequences …. (i) ARITHMETIC SEQUENCES (ii) GEOMETRIC SEQUENCES (iii) HARMONIC SEQUENCES (iv) FINBONACCI SEQUENCES
- 3. WHAT ARE FIBONACCI SEQUENCES THE FIBONACCI SEQUENCES ARE THOSE WHICH ARE DERIVED FROM FIBONACCI NUMBERS . THE FIBONACCI NUMBERS ARE 0,1,1,2,3,5,8,13,21,34,55,89,144….. THESE NUMBERS ARE OBTAINED BY ADDING THE PREVIOUS TWO NUMBERS IN ORDER TO OBTAIN THE NEXT HIGHER NUMBER… LIKE IN THE PREVIOUS EXAMPLE 0+1=1 , 1+1=2 , 2+1=3 , 3+2=5 and so on…. FORMULA FOR FIBONACCI SEQUENCE :- Fn= Fn-1 + Fn-2
- 4. SPECIALITY OF FIBONACCI SEQUENCES FIBONACCI SEQUENCES IS THE SEQUENCE WHICH CAN BE EASILY OBSERVED IN NATURE AND IT IS CONSIDERED AS ONE OF THE IDEAL SEQUENCES OF NATURE AS WELL AS MANKIND WE ALL KNOW ABOUT GOLDEN RATIO THAT IS CONSIDER AS THE NATURAL BEAUTY RATIO AND GUESS WHAT WE HAVE IT IN THE FIBONACCI SEQUENCE AS IN FIBONACCI RATIOS EVERY THIRD NUMBER IS EVEN AND THE DIFFERECE BETWEEN EACH NUMBER IS 0.618 WITH THE RECIPROCAL OF 1.618 DO THESE NUMBERS ARE “GOLDEN NUMBERS” AND “GOLDEN MEAN “….. TRULY FIBONACCI SEQUENCES TELLS US ABOUT THE BEAUTY OF THE NATURE
- 5. HISTORY IF FIBONACCI NUMBERS ▪ THE EXACT ORIGIANTION OF THIS SEQUENCE IS UNKNOWN ▪ IT IS BELIEVED THAT CONTRIBUTIONSTO THE THEORY BEGAN IN 200 BC BY INDIAN MATHEMATICIAN S WHOSE STUDIES WERE BASED IN SANSKRIT PARADOY . ▪ THE SEQUENCE WAS INTRODUCED TO WESTERN EUROPEAN MATHEMATICS IN 1202 BY LEONARDO OF PISA , aka FIBONACCI ▪ HIS STUDY OF THE SEQUENCE BEGAN WITH THE BREEDING PATTERNS RABBITS . IN WHICH HE FOUND RABBIT GENERATIONS DUBLICATED IN ACCORDANCE WITH THE FIBONACCI NUMBERS .
- 6. FIBONNACCI SEQUENCES IN NATURE EVERYONE OF US KNOW THAT HOW BEAUTIFUL OUR NATURE IS ….BUT WHAT IF I SAY THAT THIS OUR VERY OWN NATURE FOLLOWS A MATHEATICAL SEQUENCE …OK MANY THOSE WHO DO NOT LIKE MATHS WILL SAY THAT THEY ARE NOT AT ALL INTRESETED IN KNOWING PATTERN …… BUT TODAY I’LL EXPLAIN THAT PART ALSO…. SO LET’S SEE WHAT ARE THOSE ..
- 7. FIBONACCI SEQUENCE IN SUNFLOWER FIBONACCI SEQUENCE CAN BE OBSERVED IN SUNFLOWER HEADS ARRANGEMENT . THE ARANGEMENT OF SEED IS BASED UPON THE GOLDEN MEAN WHICH CORRESPONDS TO THE GOLDEN ANGKE OF 137.5°. THE SEEDS ARE ARRANGED IN A CONSISTENT PATTERNS OF 137.5° . THIS GIVES FLOWER THE OPTIMAL FILLING OF RATIO OF ITS SEEDS.
- 8. FIBONACCI SEQUENCE IN A SEASHELL THE FIBONACCI NUMBERS DIRECTLY CORRESPONDS TO THE SPIRALS FOUND IN A SUBSHELLS . THE NUMBERS FORM WHAT WE CALLED FIBONACCI RECTANGLES OR “GOLDEN RECTANGLES”. THE RECTANGLES ARE UNIQUE BECAUSE EACH RECTANGLES HAS SIDE EQUAL TO THE LENGTH OF FIBONACCI NUMBERS. WITHIN THESE RECTANGLES WE CAN CREATE A SPIRAL WITH CROSS SECTIONS EQUAL TO THE EXACTLY 1.618[“GOLDEN MEAN” WITH THE CROSSEPONDING ANGLE OF 137.5°.]
- 9. CONCLUSION FROM THIS WE CAN CONCLUDE ONE THING THAT…. WHAT WE GET IN PRESENT AND FUTURE IS NOTHING BUT THE SUM TOTAL OF OUR PREVIOUS ACTIONS……