The Golden Ratio

Speedtape

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What significance is 1.618, and how can it be applied in aeronautical engineering design?
 

makersmarc

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What? You got an aeronautics test coming up? ;-)

I don't know, but you've given me something to research. I'm a big fan of Fibonacci.
 

makersmarc

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I'm sure this is just a coincidence, but Anastasia Romanov was born on June 18th, 1901.
 

Sig

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I'm sure this is just a coincidence, but Anastasia Romanov was born on June 18th, 1901.

And she died just a few years later! 07/17/18 is almost awesome. It was a Wednesday, which happens to come before Thursday, which is what today is (in my time zone), and Arthur Dent never got the hang of Thursdays. If you add the numbers together, you get the answer! AMAZING.

I'm impressed you pulled 618 out of thin air. Pretty cool.

Andy wins for the best answer, btw.
 

Speedtape

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I'm sure this is just a coincidence, but Anastasia Romanov was born on June 18th, 1901.
Very Good! Then you may be familiar with the special features of the Great Pyramid? And, the significance of 1.618 in Italian architecture, as well as the perspective presented in the art of some of the great artists through the ages?

I'm impressed with the fact that we have some Brainiacs on F.I. It seems some are imbibing knowledge as well as occasional potable spirits.
 
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G21Agoose

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The Golden Ratio.............
 

DrewBlows

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Simple, it's the ratio of what I am making to what I should be making...
 

makersmarc

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And she died just a few years later! 07/17/18 is almost awesome. It was a Wednesday, which happens to come before Thursday, which is what today is (in my time zone), and Arthur Dent never got the hang of Thursdays. If you add the numbers together, you get the answer! AMAZING.

I'm impressed you pulled 618 out of thin air. Pretty cool.

Andy wins for the best answer, btw.
More precisely, she was born on 1-6-18.

C'mon, how about a little suspension of disbelief. Sheesh, you probably don't believe the government is covering up what happened at Roswell, or that the CIA blew up the WTC.
 

Stifler's Mom

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Or is 1.618 the ontime percentage of the VPS station since Mesaba took over?
 

WMUSIGPI

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Or is 1.618 the ontime percentage of the VPS station since Mesaba took over?
I've only been there once but they did a great job getting me turned and departed with a full flight 10 early including 2 Jumpseaters (one up front) and I was able to make my commute home rather than having to wait 4 hours for the last flight home.....
 

Raoul Duke

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Phi not Pi. Big difference - it explains why the windows on a CRJ-200 are so small:

Two quantities a and b are said to be in the golden ratio φ if:
This equation unambiguously defines φ.
The right equation shows that a = bφ, which can be substituted in the left part, giving
Dividing out b yields
Multiplying both sides by φ and rearranging terms leads to:
The only positive solution to this quadratic equation is

[edit] Relationship to Fibonacci sequence

For more details on this topic, see Fibonacci number.
http://en.wikipedia.org/wiki/File:FakeRealLogSpiral.pnghttp://en.wikipedia.org/wiki/File:FakeRealLogSpiral.png
Approximate and true golden spirals. The green spiral is made from quarter-circles tangent to the interior of each square, while the red spiral is a Golden Spiral, a special type of logarithmic spiral. Overlapping portions appear yellow. The length of the side of a larger square to the next smaller square is in the golden ratio.


http://en.wikipedia.org/wiki/File:Fibonacci_spiral_34.svghttp://en.wikipedia.org/wiki/File:Fibonacci_spiral_34.svg
A Fibonacci spiral that approximates the golden spiral, using Fibonacci sequence square sizes up to 34.


The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, … The closed-form expression (known as Binet's formula, even though it was already known by Abraham de Moivre) for the Fibonacci sequence involves the golden ratio:
The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence (or any Fibonacci-like sequence):
Therefore, if a Fibonacci number is divided by its immediate predecessor in the sequence, the quotient approximates φ; e.g., 987/610 ≈ 1.6180327868852. These approximations are alternately lower and higher than φ, and converge on φ as the Fibonacci numbers increase, and:
Furthermore, the successive powers of φ obey the Fibonacci recurrence:
This identity allows any polynomial in φ to be reduced to a linear expression. For example:
 

Sig

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The Houston Eulers were such a hard team to bet against.

The bookies made the spread naturally, and logged it as such.
 

PBRstreetgang

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I thought you said Golden Shower!




nevermind!
PBR
 

Andy Neill

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If you wanted to cut a piece of sheet metal to form the floor and sloped side of a cargo bin that was 1 unit wide at the bottom, two units high, and two units wide at the top, the length of that piece would be 2 times phi. (about 3.236 units).

Consider the coorditates of the side view of the vargo bin to be (0,0), (1,0), (2,2), and (0,2).
 
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