Originally posted by aostling
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math. machining seems to take a fare am mount of math.
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Regards, Marv
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Originally posted by cameron View PostRe post #38:
It's rather disappointing, isn't it, to find that the positive and negative golden means have the same absolute value?
Some mathematical notation expressing the equality to which you refer would be helpful.
Regards, Marv
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One of my roommates (a computer science guy, they're a little different) in college came home one day and said he'd learned that 1 + 1 can equal 3, for high values of 1. Of course we replied with the typical mockery and abuse, as expected, but the explanation actually made sense.
It has to do with rounding, and is a good (but simplified) warning not to round answers too early.
If the initial values of 1 are something like 1.3 and 1.4, they could each be approximated or rounded to 1. Then 1+1=2, right? Except the original values are actually 1.3+1.4=2.7, which can be rounded to 3.
I've always thought that was an interesting bit of math, and it sometimes applies to machining.
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Originally posted by mklotz View Post
It's not clear to what "negative golden mean" refers in your post. The mean is always reported as a positive number, 1.618...
Some mathematical notation expressing the equality to which you refer would be helpful.
This implies, I think, that there are always two solutions for a quadratic equation.
The solutions to the equation representing the golden mean are +1.618... and 1.618... . In other words, there are two golden means, a positive and a negative. The negative is usually ignored, but ignoring it does not make it go away.
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Originally posted by cameron View Post
Oops!
g = golden mean = 1.618
then
0.618 = 1  g =  1/g
Yes, there is this second root to the quadratic but, as shown above, it's simply related to what is normally referred to as the golden mean. In most cases, the mean is used to represent a ratio as sides of a rectangle to the Greeks or consecutive terms in the Fibonacci series. Negative ratios don't make much sense in the real world so this second root hasn't found many uses other than being shorthand for  1/g
Fun fact: If we define this second root as h (= 1/g), then Binet's formula allows us to write the nth term in the Fibonacci series as: Fn = (g^n  h^n) / sqrt(5)Regards, Marv
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1/0.618 = 1.618http://pauleschoen.com/pix/PM08_P76_P54.png
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Is the golden mean the same as the golden ratio?????The shortest distance between two points is a circle of infinite diameter.
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If you type "golden mean" into Wikipedia, one of the lines it returns in its disambiguation page says this...
Golden ratio, a specific mathematical ratio (sometimes called golden mean)
I've always heard it referred to as "golden mean" but this extract from Wikipedia...
The golden ratio (roughly equal to 1.618) was known to Euclid.[39] The golden ratio has persistently been claimed[40][41][42][43] in modern times to have been used in art and architecture by the ancients in Egypt, Greece and elsewhere, without reliable evidence.[44] The claim may derive from confusion with "golden mean", which to the Ancient Greeks meant "avoidance of excess in either direction", not a ratio.
suggests that we should refer to it as "ratio".
Regards, Marv
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