What is the Fibonacci Sequence & the Golden Ratio? Simple Explanation and Examples in Everyday Life

The Fibonacci sequence is a series of numbers in which a given number is the addition of the two numbers before it. So, if you start with 0, the next number will be 1, followed by 1, followed by 2, followed by 3 and so on. As you can see, every number in this series or sequence is obtained by adding the two preceding numbers. This simple series of numbers is referred to as the Fibonacci sequence for Fibonacci series. And individual numbers in this sequence are often called Fibonacci numbers.

To the uninitiated, it may just seem like a series of numbers, but the Fibonacci sequence has been discovered and rediscovered in various forms, not only in mathematics, but also in nature and our everyday lives.

There’s another exciting offshoot of the Fibonacci sequence - the golden ratio. Seashells are one of the most common examples of the golden spiral in nature. Ocean waves, hurricanes, flower buds, snail shells, spider webs are some of the many naturally-occurring examples.

#science #animation #fibonacci

Intro - (0:00)
What is the Fibonacci sequence - (0:57)
Leonardo of Pisa and the Fibonacci sequence - (1:39)
Fibonacci sequence and the Golden Ratio - (2:56)

References:

SUBSCRIBE to get more such science videos!

Follow us on Twitter!

Follow us on Facebook!

Follow our Website!

[allisonnowak]

It bothers me that the visuals show the incorrect sequence (0, 1, 2, 3...). Shouldn't it be 0, 1, 1, 2, 3...? (Example of incorrect at 1:35 and 2:36.)

[gmwell]

Excellent presentation, the one place that everybody seems to miss is that the Fibonacci sequence is also found inside the programming of the human brain, your brain automatically tells you whether somebody's face and body fits inside the Fibonacci sequence because you determine them to be handsome or pretty based on the closeness of the math formula in the facial structures or the body... So if the eyes are too far apart and the ears are not in the right place your brains programming automatically tells you that person's out of mathematical Harmony.. the Divine ratio programmed in the brain.

[Scienceabc]

Do you encounter the golden ratio in your everyday life? If you have some more examples, then do share them with others in the comment section below.

[DineshKumar-uwfp]

Beautifully presented and very well elaborated. "SHORT AND PRECISE"!! This video is so easy to understand the Fibonacci sequence and the golden ratio. Good Work!!

[avtpro]

I never called it Fibonacci, just the Golden Ratio. Learned something new. Thanks.

[Anamnesis]

You left out financial markets. Fibonacci retracement is a technical analysis method used to predict (with alarming accuracy) the various levels of support and resistance when trading equities and assets. It isn't portrayed as a spiral on a pricing chart, but the ratio principle remains the same. And since markets are ultimately an indicator about public sentiment over the value of something, it shows how the Fibonacci Sequence applies to human psychology and emotion too.

[shoecake]

I love this. The workings of the universe in an equation. When I first heard of this, I couldn’t help but to count petals, and would tell anyone who’d listen!

[_s]

I forgot when I subscribed to this channel and this is the first video I viewed after subscribing, I really like it.Our professor taught us how to write Fibonacci sequence in c

[KenMiddletonUkulele]

In music e.g. intervals between the notes of the major chord, notes of the harmonic series on brass instruments, serial (12 tone) music, etc.

[celestineP]

If it was described by Indians in the 6th Century, and Fibonacci merely translated the concepts, shouldn’t it be called by the original name - as the Pingala sequence?

[daniesavage]

I love that it dates back to the 6th century in India. I wonder how long it’s been studied. Love the history of science. Shouts out to India and any other culture who may have known about this ❤. Fascinating 🐌🐌

[mohanpathak]

All animations are supreme. Such an informative and entertaining video. You make a great contribution to science.

[Junkinsally]

The only reason matter manifests as a spiral is because the universe and everything in it are spinning. The “divine ratio” is just a visual representation of the rate of that spin.

[jefersonmachado]

Excellent teaching, Fibonacci also has full application in financial assets, mainly on the Index, and high volatility assets.

[fgdart]

Great work! I watched many videos byt this one was very clear and well explained! Thank you

[chimpmonk]

im sorry, im not really intelligent, but i can't seem to figure out 4:33, how or where exactly do you see the spiral? Even with the guidelines, i still can't figure it out

[mayahewitt]

Now I can learn to spin my steel balls

[williamseifert]

Use this ratio when you're brewing your coffee and you will achieve the perfect cup. For example, 1.6 tablespoons of coffee grounds per 6 oz of water. If you use Kcups, which have about 2 tablespoons of grounds in them, then the ratio is 1 Kcup per 7.5 ounces of water.

You're welcome.

[carlosalexandreFAT]

The association of the main numbers in the field of mathematics with each other, reflects numerical sequences that correspond to the dimensions of the Earth, the Moon, and the Sun in the unit of measurement in meters, which is: 1' (second) / 299792458 m/s (speed of light in a vacuum).

Ramanujan number: 1, 729
Earth's equatorial radius: 6, 378 km.
Golden number: 1.61803...
• (1, 729 x 6, 378 x (10^-3)) ^1.61803 x (10^-3) = 3, 474.18
Moon's diameter: 3, 474 km.

Ramanujan number: 1, 729
Speed of light: 299, 792, 458 m/s
Earth's Equatorial Diameter: 12, 756 km. Earth's Equatorial Radius: 6, 378 km.
• (1, 729 x 299, 792, 458) / 12, 756 / 6, 378) = 6, 371
Earth's average radius: 6, 371 km.

The Cubit
The cubit = Pi - phi^2 = 0.5236
Lunar distance: 384, 400 km.
(0.5236 x (10^6) - 384, 400) x 10 = 1, 392, 000
Sun´s diameter: 1, 392, 000 km.

Higgs Boson: 125.35 (GeV)
Phi: 1.61803...
(125.35 x (10^-1) - 1.61803) x (10^3) = 10, 916.97
Circumference of the Moon: 10, 916 km.

Golden number: 1.618
Golden Angle: 137.5
Earth's equatorial radius: 6, 378
Universal Gravitation G = 6.67 x 10^-11 N.m^2/kg^2.
(((1.618 ^137.5) / 6, 378) / 6.67) x (10^-20) = 12, 756.62
Earth’s equatorial diameter: 12, 756 km.

The Euler Number is approximately: 2.71828...
Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2. Golden number: 1.618ɸ
(2.71828 ^ 6.67) x 1.618 x 10 = 12, 756.23
Earth’s equatorial diameter: 12, 756 km.

Planck’s constant: 6.63 × 10-34 m2 kg.
Circumference of the Moon: 10, 916.
Gold equation: 1, 618 ɸ
(((6.63 ^ (10, 916 x 10^-4 )) x 1.618 x (10^3)= 12, 756.82
Earth’s equatorial diameter: 12, 756 km.

Planck's temperature: 1.41679 x 10^32 Kelvin.
Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2.
Speed of Sound: 340.29 m/s
(1.41679 ^ 6.67) x 340.29 - 1 = 3, 474.81
Moon's diameter:: 3, 474 km.

Cosmic microwave background radiation
2.725 kelvins, 160.4 GHz,
Pi: 3.14
Earth's polar radius: 6, 357 km.
((2, 725 x 160.4) / 3.14 x (10^4) - (6, 357 x 10^-3) = 1, 392, 000
The diameter of the Sun: 1, 392, 000 km.

Numbers 3, 6 & 9 - Nikola Tesla

One Parsec = 206265 AU = 3.26 light-years = 3.086 × 10^13 km.
The Numbers: 3, 6 and 9

((3^6) x 9) - (3.086 x (10^3)) -1 = 3, 474
The Moon's diameter: 3, 474 km.

Now we will use the diameter of the Moon.
Moon's diameter: 3, 474 km.
(3.474 + 369 + 1) x (10^2) = 384, 400
The term L.D (Lunar Distance) refers to the average distance between the Earth and the Moon, which is 384, 400 km.

Moon's diameter: 3, 474 km.
((3+6+9) x 3 x 6 x 9) - 9 - 3 + 3, 474 = 6, 378
Earth's equatorial radius: 6, 378 km.


Orion: The Connection between Heaven and Earth eBook

[waywardboundband]

I bought my wife an ammolite(opalized ammonite) pendant for her up coming birthday. It's a spectacular example of the golden ratio!