Fun with numbers
Introduction
Hi friends,
My name is Yunus Poonawala , I study at Hasanat High School in standard 9 and my hobbies are to cycle, swimming and photography.
My name is Yunus Poonawala , I study at Hasanat High School in standard 9 and my hobbies are to cycle, swimming and photography.
Hello,
My name is Fakhruddin Unwala .I study in Hasanat High School in standard 9. I like to play football and my ambition is to become a footballer.
My name is Fakhruddin Unwala .I study in Hasanat High School in standard 9. I like to play football and my ambition is to become a footballer.
Hi,
My name is Maurvi Kotwal . My hobby is to draw through which I express my emotions.
My name is Maurvi Kotwal . My hobby is to draw through which I express my emotions.
Ahoy,
My name is Hatim Yusuf Savai and I am 13 years old. my hobbies are: cycling, swimming and reading. My favourite subjects in school are :- chemistry and mathematics. I am not good at sports but I am good at my study and always try to score good marks. My goal in life is to become an architect or an interior designer.
My name is Hatim Yusuf Savai and I am 13 years old. my hobbies are: cycling, swimming and reading. My favourite subjects in school are :- chemistry and mathematics. I am not good at sports but I am good at my study and always try to score good marks. My goal in life is to become an architect or an interior designer.
Hello ,
My name is Husain Mustafa Chittalwala. I study in standard 9 at Hasanat High School. My hobby is to cook and I enjoy playing throw ball .
My name is Husain Mustafa Chittalwala. I study in standard 9 at Hasanat High School. My hobby is to cook and I enjoy playing throw ball .
ACTION PLAN
Group leader: yunus poonawala.
Editor WEEBLY: Yunus poonawala.
Photographer: Fakhruddin Unwala.
Video editor: Yunus poonawala.
Questionnaires: Maurvi kotwal.
Interviews: Husain chitalwala.
Writing reports/Summarizing answers: Hatim sawai.
Other tasks: All.
Editor WEEBLY: Yunus poonawala.
Photographer: Fakhruddin Unwala.
Video editor: Yunus poonawala.
Questionnaires: Maurvi kotwal.
Interviews: Husain chitalwala.
Writing reports/Summarizing answers: Hatim sawai.
Other tasks: All.
FIBONACCI SEQUENCE
Fibonacci's sequence - denoted by the formula given above - was first given by LEONARDO BONACCI also called FIBONACCI - he was an italian matematician considerd to be the most talented matematician of the Middle ages - gave the sequence as 0,1,1,2,3,5,8,13, 21, 34, 55, 89, 144, 233, 377, ... . The next term of the sequence is found by adding the two previous terms of the sequence like 1,2,3 [2 + 1 = 3]
Properties of Fibonacci's sequence
Formula:- x=1+1/x
Limit:- (1+√5)/2 = ϕ = 1.618033988 = 2sin(54) = Golden ratio
Number of digits:- ∞
GOLDEN RATIO AND FIBONACCI'S SEQUENCE
The Golden Ratio is closely related to the fibonacc's sequence in the following way
1) it is the Limit of the Fibonacci's sequence
2) The Fibonacci's tiles give a golden spiral (photo on right)
1) it is the Limit of the Fibonacci's sequence
2) The Fibonacci's tiles give a golden spiral (photo on right)
GOLDEN RATIO (INVISIBLE YET OMNIPRESENT)
The golden ratio or the divine propotion or the golden number- given by the above formula - was first used in the parthenon in 430 BC. Two quantities are said to be in the golden ratio if if their ratio is the same as the ratio of their sum to the larger of the two quantities. This simple ratio has been fascinating people since ages as it is found almost every where and very closely related to fibonacci's sequence.
GOLDEN RATIO IN THE FIBONACCI'S SEQUENCE
As discussed above the Golden Ratio is the limit of the Fibonacc's sequence that means that the quotient of two consequtive integers of the fibonacc's sequence is approximately equal to phi and the closeness increases with the increase in the numbers.
A |
B |
B/A |
2 |
3 |
1.5 |
3 |
5 |
1.666 |
5 |
8 |
1.6 |
8 |
13 |
1.625 |
... |
... |
... |
144 |
233 |
1.618055556 |
233 |
377 |
1.618025751 |
The fibonacci tiles give out a golden rectangle and a golden spiral
GOLDEN RATIO IN GEOMETRY
Golden ratio is found abundantly in geometrical figures out of which the simplest include a golden rectangle a pentagon and a golden line
PENTAGON
The diagnals of a pentagon are φ times its sides i.e. diagnal = φs
GOLDEN LINE SEGMENT
The Golden segment is the most basic form of the golden ratio division which fulfills the equation "(a + b)/a = a/b"
GOLDEN RECTANGLE
The golden rectangle is a rectangle in which the sides of it are in the ratio 1: φ
It is widely used in architecture and paintings like the Mona Lisa and many paintings of Salvador Dali.
It is widely used in architecture and paintings like the Mona Lisa and many paintings of Salvador Dali.
GOLDEN RATIO IN NATURE
Golden ratio is found every where in nature but here we take two examples : The Sunflower and The shell of the snail
Sunflower
The seeds of the sunflower are arranged in spirals that are golden turns and their petals also grow in Fibonacci numbers
SHELL
There is a huge controveresy about this thing that a nautilus shell contains a golden spiral or not and the answer is no and yes both. I mean that the nautilus shell has a golden spiral but not the traditional one mentioned above. But it has a different kind of golden spiral that people call it the traditional spiral which forms the golden ratio in every 90° but our "non traditional spiral makes a golden turn every 180° so therefore it is different.
CONCLUDING φ
From the above statements and proofs we can say that φ is EVERYWHERE I mean EVERYWHERE . Any where you look you find φ we didn't have the time to do it but if we had then we would have definitelty did it . There are as many examples of φ as many numbers are there in φ like in sports in arts in achitecture and in yourself (try dividing the height of your face by the width of it) etc. It is an amazing simple ratio that has been intruiging people for aeons and noo one has ever been sucessful in completely unveiling it
SHAPES WITH NUMBERS
INTERVEIWS
Question 1: what do you think is golden ratio according to you if you don't know then please guess
ANS1 by satawat pawar: "I am not familiar with it but it has to be a ratio"
ANS2 by Rakesh mishra : "Some ratio kind of thing indispensible in daily use . Invisible yet omnipresent"
ANS3 by Suraiya : "Ratio which determines the purity of gold"
ANS4 by Saleh : "Golden ratio is a ratio of dimensions formed in nature"
Question 2 : have you got any idea about the fibonacci's sequence? If yes what is it if no then what do you think it is?
ANS1 by satawat pawar : "A mathematical sequence which is 1,1,2,3,5,8,13"
ANS2 by Rakesh mishra : "Something to do with the Golden ratio"
ANS3 by Suraiya : "Has to do something with some complex calculations in maths"
ANS4 by Saleh : "Faint childhood memory of something like 1+1+2+3+5"
Question 3 : Is maths fun?
ANS1 by satawat pawar : "yes ,absolutely"
ANS2 by Rakesh mishra : "No , not according to me"
ANS3 by Suraiya : "Yes"
ANS4 by Saleh : "undoubtedly"
Question 4 : Where is the golden ratio found (If you don't know then guess it)
ANS1 by satawat pawar: "Maybe everywhere"
ANS2 by Rakesh mishra : "I told you before I have no idea"
ANS3 by Suraiya : "United States of America"
ANS4 by Saleh : "Nature"
After the interveiws we made people aware of what exactly Golden Ratio is where it is found and also made the people aware about the Fibonacci's sequence and ts relation with the Golden ratio.