1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aliya0001 [1]
3 years ago
5

Fibanachi's racio. What is it?

Physics
1 answer:
Rainbow [258]3 years ago
8 0

Before I tell you about the Fibonacci Ratio, I have to tell you first about the Fibonacci Series.

It's named for the guy who invented it ... Leonardo Pisano Bigollo Fibonacci, an Italian mathematician born in 1170 in Pisano, Italy.

The "Fibonacci Series" is a very special series of numbers.  We find things that proceed according to the Fibonacci Series all around us in Nature, and it's used in Art and Architecture.

To make the Fibonacci Series of numbers, first write down " 0, 1 ".  After that, add as many more numbers to the series as you want.  Get EACH new number by ADDING the last two numbers that you already have.  So the first 12 numbers of the series are:

0,   1,   1,   2,   3,   5,   8,   13,   21,   34,   55,   89  . . . . .

Each number is the SUM of the 2 numbers just before it.  Pretty easy.  But it has at least a thousand interesting things about it.  There have been whole books written about the series, and about the 'Fibonacci Ratio' that comes from the series.

Now for the Fibonacci Ratio:

A ratio is what you get when you divide two numbers.  Every fraction is a ratio.  Like, the ratio of 1/2 is 1÷2 = 0.5 .  The ratio of 2/5 is 2÷5 = 0.4 .  The ratio of a person's arms to legs is 2/2 = 1 .

To get the Fibonacci Ratio, take any pair of neighboring numbers in the Fibonacci Series and divide them.  

The first pair is (0, 1).  Their ratio is (0/1) = 0.  Not too interesting.

The next pair is (1, 1).  Their ratio is (1/1) = 1.  Still not very interesting.

The next pair is (1, 2).  Their ratio is (1/2) = 0.5 .  Weird.

The next pair is  (2, 3).  Their ratio is (2/3) = 0.66..  Is something happening ?

The next pair is (3, 5).  Their ratio is (3/5) = 0.60 .  something is definitely happening.

The next pair is (5, 8).  their ratio is (5/8) = 0.6250 .  Now they're sticking around 0.6 ?

The next pair is (8, 13). Their ratio is (8/13) = 0.6154 .  wow

The next pair is (13, 21).  Their ratio is (13/21) = 0.6190  not changed much

The next pair is (21, 34).  Their ratio is (21/34) = 0.6176  changed even less

The 11th pair is (55, 89). their ratio is (55/89) = 0.6180  smaller change

As you go along and keep taking the ratio of two neighbors in the Fibonacci Series, it almost looks like they're getting closer and closer to some special number where they want to settle down.  And that is true.  We've only looked at 11 pairs in the Fibonacci series, and their ratio is already settling down and changing very little from one pair to the next.

The number they're heading for is (1/2) · (1 + √5) .  

This is the "Golden Ratio".  It's the first ratio you get when you play around with the Fibonacci Series, like I just started showing you.

You can never write it down exactly with only numbers, because √5 is an "irrational number" that can never be completely written down as a decimal.  But you can get as close to it as you want to be, by using a longer piece of the Fibonacci Series, and carrying out the division to more decimal places.

A few weird things about it:

-- Take the number.  Divide 1 by it.  Add 1 to the answer.  You've got the number again.    [  F = 1/F + 1 ]

-- Since the time of the ancient Greeks, people have always felt that this number is the way to draw and shape things that are most pleasing to us.  

-- The (length/width) of several ancient Greek buildings is the Fibonacci Ratio.  

-- The dimensions of the face of the "Mona Lisa" painting by Leonardo DaVinci have the Fibonacci Ratio in them.  

-- If a snow plow starts out at 12:00 in a steadily-falling snow, and plows equal volumes of snow in equal amounts of time, and is able to make 2 miles of progress in the first hour and 1 mile of progress in the second hour, then the snow started falling (the Fibonacci Ratio of an hour) before 12:00 .

-- The leaves sprout out of a willow-tree twig in directions that are distributed according to the Fibonacci Series.

-- The patterns of markings on the back of a turtle's shell have the Fibonacci Ratio in them.

. . . and thousands of other Fibonacci things in nature.  You should go on line and read about some of them.

= = = = = = = = = =

The 20th pair in the Fibonacci Series:  (4181, 6765).

Some approximate numbers:

Their ratio is (4181, 6765) = 0.61803399...

The reciprocal is (6765/4181) = 1.61803396...

(1/2) (1 + √5) = 1.61803398...

1 / 1.61803399 = 0.6180398...  


You might be interested in
A 45.0 kg ice skater needs a 25 N horizontal force to get moving on a smooth ice surface. What is the coefficient of friction be
SVEN [57.7K]
The horizontal force : f = k*N
k- coefficient of friction
k = f /N
N = m * g = 45 kg * 9.81 m/s² = 441.45 N
k = 25 N : 441.45 N = 0.057
Answer C) 0.057
7 0
2 years ago
A car traveled north 25 km for 1 hour. The car’s SPEED is 25 km/hr north.
kramer

Answer:

hgk

Explanation:

6 0
3 years ago
Which of the following is a good scientific question? A. Are dragons lizards or birds? B. How do star fish fall in love? C. Does
Wittaler [7]
<span>C. Does eating less fat increase a mouse's lifespan?
(If a mouse eats less fat in its meals then will it live longer: compared to other mice lives.

</span>This is a testable question that can be answered by designing and conducting an experiment.

I think D could be correct as well.

My final answer is D.


6 0
3 years ago
Read 2 more answers
Please help me this is important!
Mariulka [41]
145 Grams!
It asks for the “Total Mass” basically asking to add, If you add 20 to 125, you get 145! Correct me if im wrong
4 0
3 years ago
A short 6061-T6 aluminum cylindrical block, having an original diameter of 20mm and a length of 75mm, is placed in a compression
Alex Ar [27]

Answer:

hi apner how is ur going for the weekend on your way home

Explanation:

hi there is that something you could help me

5 0
3 years ago
Other questions:
  • Answer please I need help
    8·1 answer
  • #1. A car moving at the rate of 65 miles per hour passes a truck moving in the same direction at 38 miles per hour . What is the
    15·1 answer
  • The air pressure inside the tube of a car tire is 430 kPa at a temperature of 13.0 °C. What is the pressure of the air, if the t
    5·1 answer
  • In the 1980s, the term picowave was used to describe food irradiation in order to overcome public resistance by playing on the w
    7·1 answer
  • A thin plastic rod of length 2.5 m is rubbed all over with wool, and acquires a charge of 75 nC, distributed uniformly over its
    6·1 answer
  • 6. how do the number of electrons flowing into a light bulb compare to the number of electrons flowing out of it?
    13·1 answer
  • Large sections of troposphere with same temperature and humidity is called
    12·1 answer
  • A vertical piston-cylinder device initially contains 0.1 m^3 of air at 400 K and 100 kPa. At this initial condition, the piston
    13·1 answer
  • Which of the following is an example of the law of multiple proportions?
    9·1 answer
  • The cricket ball has a mass of 0.16kg and it hits the bat with a speed of 25 m/s. After being in contact with the bat for 0.0013
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!