Math Encounters -- Fibonacci & the Golden Ratio Exposed -- Keith Devlin (Presentation & Workshop)

The golden ratio is a fascinating number, but how much of what you read (or believe) is true—and what are the common myths? Join us as Stanford mathematician, award-winning author, and NPR "Math Guy" Keith Devlin examines the evidence and separates fact from fiction.

Devlin received a special introduction from Jim Simons, founder of Renaissance Technologies and winner of the Veblen Prize in Geometry.


Video created by Peter Barton.

[alank]

Save time: Watch from minute 5 to 15, then skip to minute 40.

[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

[phoenix]

Even if no one purposefully used the golden ratio in architecture it is still there and therefore it can be said that the ratio is deeply integrated into our world.

[ToneSpectra]

It seems unreasonable to assume humans would be able to distinguish such a precise ratio of 1:1.618 by eye anyway. I know people who don't notice if the telly is on the wrong aspect ratio! Personally, I suspected that it's actually 1:1.5 (approximately) that had some appeal. That said, if some trees and plants are beautiful because their leaves are distributed optimally, then in a way, surely we are sort of appreciating an expression of the Fibonacci sequence at least? Or is it just efficiency we appreciate?

[nzpers]

I see lots of criticism here. Like someone said it depends on what you expect. I guess to be fair, what Kevin is trying to convey is that enough examples of GR and FN are obtaining in nature that we need force it thru artificially created ones or explain them by force fitting logic in hindsight. Does it need 90 minutes to do that? well you got to see he is a professor and so cannot stop till ninety minutes once he starts! :)

[jelenagagula]

The significance behind The Last Supper has to do with perspective, which was largely absent from popular art of the time. By including perspective in work he was proving infinity, and by doing so while depicting a revered religious story he was essentially saying "neener neener neener" or "actually much of what transcendental christians believe is untrue, and i've proved it here, in this painting, which you ironically love."

[robertgreen]

If this were the case, please explain the following. Why do I get angry. Why do my emotions change based on others peoples emotions. Why do colors and noises effect my emotions. Why do my emotions effect other people. Where do emotions exist in the material world? How do invisible non-existent energy fields (as you claim) affect others or transfer from one to another? Why does one's thought interfere with quantum experiments? I could go on, but this should be enough for now.

[ericespinoza]

These camera men though lmao. It's so distracting. They just keep zooming in on faces :|

[kandysman]

47:00  bs.  just a quick google search, find loads of modern architects using the golden ratio.

[LufeLima]

I am not a mathematician, but I am a musician and know that the musical scale is based on this proportion  e.g.: Each fret on a guitar follow this ratio.

[thinkpad]

Irrational numbers can be defined. Pi, e, phi, the square root of 2... all very well defined. They just can't be expressed in terms of ratios of integers.

[naedolor]

for example there is evidence to support the theory that some of the greatest painters that ever lived have used Camera Obscura after the availability of mirrors and lenses. The whole point of art is to raise questions and create intrigues. Subtle framing, straight lines, diagonals and the golden ratio play key factors in the essential narrative of a painting and that is FACT with the note that these are not rules, but guidelines and they are not always all applied concurrently.

[thinkpad]

You seem to have an incorrect understanding of definition. Numbers are not defined by their ability to be written out one way or another. Consider the number 25^86532. This number has far more digits than there are atoms in the universe; writing it out as a decimal or ratio of integers is physically impossible. But it's an integer. All numbers are symbols; the important thing for a definition is that we precisely understand their quantity, not that we can necessarily write it as a decimal.

[robertgreen]

Actually. The Pyramids were built using ancient knowledge that we have long forgotten. This is to include sacred geometry. They also knew how to nullify the weight of the gigantic limestone slabs they used. This was proven by the man who built the Coral Castle found in Florida. Look it up and expand your mind,

[partsofone]

Just a note to intelligent design proponents (like myself): Don't assume it's a good idea to dislike this video before watching the entire thing. It's not what you probably think it is. In fact I'll even give you a spoiler: At the end (and actually well before then) he says the golden ratio is the most wonderful number in the world.

[naedolor]

I totally agree with Mr. Devlin that we can see patterns where there are none BUT in the same time Mr. Devlin is trying to quantify art using science which is almost a paradox. The golden ratio was studied in art schools for hundreds of years, even though it wasn't called that. An artist will never reveal his secrets or his craftsmanship except to a selected few if any;

[fuentes]

That would be great if the donation dropdown had the fibonacci series in it :)

[neoiko]

A very big % of his debunkings are based on the assumption that there isn't a margin of error.

I think there are often confirmation-biases at work... so people DO tend to over-represent it... but there's also a margin-of error... so there's kindof a gravity-well pointing towards 1.618... not dissimilar to the way the ratio between adjacent fibonacci numbers converges on phi. But art isn't exact. Nature isn't exact. Doesn't mean there isn't a tendency

[nonyabidness]

Amazing how a scientist can give a lecture where he says, what I used to say was the truth but now I know it wasn't because what I am saying is now is actually the real truth. How does one keep a straight face?

[TheEla]

loved it.... great talk and great humor :)