I wanted use 'Go Into' for 'Do Unto' but that gave the reciprocal value.
Irregular Webcomic! #5309
18 hours ago
Thursday, September 08, 2011
Golden
(Click on the cartoon to see the full image.)
(C)Copyright 2011, C. Burke. All rights reserved.
I wanted use 'Go Into' for 'Do Unto' but that gave the reciprocal value.
I wanted use 'Go Into' for 'Do Unto' but that gave the reciprocal value.
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4 comments:
If you use "go into the other part as the whole would go into you", you get (1-x)/x = x/1, which is the same equation x^2 = (1-x) that you have here.
The bigger problem is that the comic is wrong. :-(
The solution to x^2 = (1-x) is (sqrt(5)-1)/2, which is the conjugate of the golden ratio (sqrt(5)+1)/2.
How about this? "Go into another as you would have 1 go into you" to mean (1+x)/x = x/1, which gives x^2=(1+x) which *is* the golden ratio.
Works for me. This is what I get for coming up with comics during mandatory professional development.
Anyway, I thought I'd double-checked it properly, replacing the a, b and a + b.
Oh, well. Off to school now.
Well, I have an equation that gets up there anyway.
I started with the proportion (a/b) = (a+b)/a, straight out of wikipedia.
To fit it into the comic, I swapped a with x, a+b with 1, which made b = 1 - x.
The problem comes from using the letter "x", which when solved for gives the conjugate. HOWEVER, each of the two ratios in the original proportion are equal the Golden Ratio.
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