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Old 21st January 2005, 10:08 PM   #11
AndyN is offline AndyN  United States
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Quote:
Originally posted by markp
Actually, there are many 'golden ratios'. The idea behind them is that the product of all the dimensions is equal to 1. Notice that .6x1x1.6=1 and .8x1x1.25=1 and so on.

Yes, but Phi is not 1.6 exactly - it's irrational, (the 'most' irrational number in fact, beacuse it expands into more fractions ) and so it cannot feature in a set that sums to one.

(Unless, does the irrationality of the 1/Phi side of a golden rhombus negate the irrationality of Phi side? dunno.)

Either way, my mitre saw doesn't have a detent for the square root of 2, so the infinite series part of the measurement gets rounded off in the kerf. My point is theoretical, not practical.

In my understanding, the use of the term 'golden' denotes the presence of the ratio Phi (1.619...) so while the "golden ratio" may sum to 1, and other ratios may sum to 1, the golden designation is not conferred upon the others..

I am not a mathemetician, so I'm likely wrong... if I am, please explain more.

--humbly, Andy
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Old 22nd January 2005, 03:11 AM   #12
eLarson is offline eLarson  United States
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There's a book out called "The Golden Ration: The story of PHI, the world's most astonishing number". (1/137's pretty good, too, but I digress.) Y'all might like it.

(The ratio can be found in all manner of living things, just by virtue of the way they grow... the nautilus shell is probably the most famous version... see Cardas.)
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Old 22nd January 2005, 10:31 AM   #13
markp is offline markp  United States
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Quote:
Originally posted by AndyN



Yes, but Phi is not 1.6 exactly - it's irrational, (the 'most' irrational number in fact, beacuse it expands into more fractions ) and so it cannot feature in a set that sums to one.

(Unless, does the irrationality of the 1/Phi side of a golden rhombus negate the irrationality of Phi side? dunno.)

Either way, my mitre saw doesn't have a detent for the square root of 2, so the infinite series part of the measurement gets rounded off in the kerf. My point is theoretical, not practical.

In my understanding, the use of the term 'golden' denotes the presence of the ratio Phi (1.619...) so while the "golden ratio" may sum to 1, and other ratios may sum to 1, the golden designation is not conferred upon the others..

I am not a mathemetician, so I'm likely wrong... if I am, please explain more.

--humbly, Andy
I am speaking practically not theoretically. Also take a look at the Fibonacci series for another explaination.
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Old 22nd January 2005, 05:29 PM   #14
GM is offline GM  United States
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I am speaking practically not theoretically.
FWIW in the few audio books I have that discuss this, there's only one golden ratio, with the rest being desirable acoustic ratios.

GM
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Old 21st February 2012, 05:22 PM   #15
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Has anyone ever heard of the Golden Rule in speaker box building? I heard something about this and the formula is supposed to be 0.6 x 1.0 x 1.6
Just to record, the Golden Ratio is 1 x 1.618 x 2.618
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Old 21st February 2012, 07:17 PM   #16
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Just to record, the Golden Ratio is 1 x 1.618 x 2.618
The ratio is usually defined by 0.618 to 1 to 1.618. This makes the math easier & more elegant since 1/0.618 = 1.618 (to 3 digits, phi is an irrational number with infinite number of digits in the decimal expansion)

0.618:1:1.618 x 1.618 = 1:1.618:2.618

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Old 21st February 2012, 08:11 PM   #17
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Golden ratio: The higher the ratio of gold to 'filler' metals, the more it costs.
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Old 21st February 2012, 08:15 PM   #18
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Old 21st February 2012, 10:26 PM   #19
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Originally Posted by planet10 View Post
The ratio is usually defined by 0.618 to 1 to 1.618. This makes the math easier & more elegant since 1/0.618 = 1.618 (to 3 digits, phi is an irrational number with infinite number of digits in the decimal expansion)

0.618:1:1.618 x 1.618 = 1:1.618:2.618

dave
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Old 12th June 2013, 03:12 PM   #20
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Oh so stinky bad. Translational mode analysis of a prismatic space (rectangles) provides the most spreading of resonances with a ratio of 1.1.414x1.732. Square root of 1x2x3. There has been a lot of nonsense published about this considering some single aspect which misses the translational modes and only considers the main modes. But then wrong is always the most popular.
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