All categories

3 years ago

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

how much gravitational potential energy do you give a 70 kg person when you lift him up 3 m in the air?

SCORPION-xisa [38]

Given gravitational potential energy when he's lifted is 2058 J.

Kinetic energy is transferred to the person.

Amount of kinetic energy the person has is -2058 J

velocity of person = 7.67 m/s².

<h3>Explanation:</h3>

Given:

Weight of person = 70 kg

Lifted height = 3 m

1. Gravitational potential energy of a lifted person is equal to the work done.

$PE_g=W=m\times g\times h\\Acceleration due to gravity = g = 9.8 \ m/s^2 \\PE_g= m = m\times g\times h= 70\times 9.8 \times 3 = 2058\ kg.m/s^2 = 2058\ J$

Gravitational potential energy is equal to 2058 Joules.

2. The Gravitational potential energy is converted into kinetic energy. Kinetic energy is being transferred to the person.

3. Kinetic energy gained = Potential energy lost = $-PE_g = -2058\ kg.m/s^2$

Kinetic energy gained by the person = (-2058 kg.m/s²)

4. Velocity = ?

Kinetic energy magnitude= $\frac{1}{2} m\times v^2 = m\times g \times h$

Solving for v, we get

$v=\sqrt{2gh} =\sqrt{2\times 9.8 \times 3} = \sqrt{58.8} = 7.67 m/s^2$

The person will be going at a speed of 7.67 m/s².

4 0

3 years ago

A steel ball rolls with a constant velocity on a tabletop 0.950 m high it rolls off and hit the ground 0.352 m from the edge of

sp2606 [1]

Answer:

0.799 m/s if air resistance is negligible.

Explanation:

For how long is the ball in the air?

Acceleration is constant. The change in the ball's height $\Delta h$ depends on the square of the time:

$\displaystyle \Delta h = \frac{1}{2} \;g\cdot t^{2} + v_0\cdot t$ ,

where

$\Delta h$ is the change in the ball's height.
$g$ is the acceleration due to gravity.
$t$ is the time for which the ball is in the air.
$v_0$ is the initial vertical velocity of the ball.

The height of the ball decreases, so this value should be the opposite of the height of the table relative to the ground. $\Delta h = -0.950\;\text{m}$ .
Gravity pulls objects toward the earth, so $g$ is also negative. $g \approx -9.81\;\text{m}\cdot\text{s}^{-2}$ near the surface of the earth.
Assume that the table is flat. The vertical velocity of the ball will be zero until it falls off the edge. As a result, $v_0 = 0$ .

Solve for $t$ .

$\displaystyle \Delta h = \frac{1}{2} \;g\cdot t^{2} + v_0\cdot t$ ;

$\displaystyle -0.950 = \frac{1}{2} \times (-9.81) \cdot t^{2}$ ;

$\displaystyle t^{2} =\frac{-0.950}{1/2 \times (-9.81)}$ ;

$t \approx 0.440315\;\text{s}$ .

What's the initial horizontal velocity of the ball?

Horizontal displacement of the ball: $\Delta x = 0.352\;\text{m}$ ;
Time taken: $\Delta t = 0.440315\;\text{s}$

Assume that air resistance is negligible. Only gravity is acting on the ball when it falls from the tabletop. The horizontal velocity of the ball will not change while the ball is in the air. In other words, the ball will move away from the table at the same speed at which it rolls towards the edge.

$\begin{aligned}\text{Rolling Velocity}&=\text{Horizontal Velocity} \\&= \text{Average Horizontal Velocity}\\ &=\frac{\Delta x}{\Delta t}=\frac{0.352\;\text{m}}{0.440315\;\text{s}}=0.0799\;\text{m}\cdot\text{s}^{-1}\end{aligned}$ .

Both values from the question come with 3 significant figures. Keep more significant figures than that during the calculation and round the final result to the same number of significant figures.

3 0

3 years ago

5) Find the initial velocity for a 700 kg car that

Serhud [2]

Answer:

Δv = 12 m/s, but we are not given the direction, so there are really an infinite number of potential solutions.

Maximum initial speed is 40.6 m/s

Minimum initial speed is 16.6 m/s

Explanation:

Assume this is a NET impulse so we can ignore friction.

An impulse results in a change of momentum

The impulse applied was

p = Ft = 1400(6.0) = 8400 N•s

p = mΔv

Δv = 8400 / 700 = 12 m/s

If the impulse was applied in the direction the car was already moving, the initial velocity was

vi = 28.6 - 12 = 16.6 m/s

if the impulse was applied in the direction opposite of the original velocity, the initial velocity was

vi = 28.6 + 12 = 40.6 m/s

Other angles of Net force would result in various initial velocities.

5 0

2 years ago

A crate falls from an airplane flying horizontally at an altitude of 2,000 m.

Hatshy [7]

Answer:

20.2 seconds

Explanation:

The airplane (and therefore the crate) initially has no vertical velocity, so v₀ = 0 m/s.

The crate is in free fall, so a = -9.8 m/s².

The crate falls downward, so Δx = -2000 m.

Find: t, the time it takes for the crate to land.

Δx = v₀ t + ½ at²

-2000 m = (0 m/s) t + ½ (-9.8 m/s²) t²

t = 20.2 s

It takes 20.2 seconds for the crate to land.

7 0

3 years ago

Use the drop-down menus to identify the parts of DNA. Label A: Label B:

love history [14]

Label A:

Nitrogen bases

Label B:

Sugar-phosphate backbone

7 0

2 years ago

Read 2 more answers