## Thursday, September 08, 2011

### Golden

(Click on the cartoon to see the full image.)

I wanted use 'Go Into' for 'Do Unto' but that gave the reciprocal value.

S said...

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.

S said...

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.

(x, why?) said...

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.

(x, why?) said...

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.