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.
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.
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.
ReplyDeleteThe 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.
ReplyDeleteWorks for me. This is what I get for coming up with comics during mandatory professional development.
ReplyDeleteAnyway, 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.
ReplyDeleteI 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.