Re: Great Book
Posted by cougar on Feb 28, 2002 at 18:48
(67.40.100.61)Re: Great Book (Pasti)
I hope you do realize that according to your algebraic definition, there are two golden ratios, since the equation is quadratic.
Yes, that's right, but looked at in the right way, the two solutions are the same.
- One solution is +1.618. When you square this, you get 2.618... Which is exactly 1 more than 1.618.
- The other solution is -.618. Square that and you get +.382... again exactly 1 more than -.618.
The golden ratio is visualized by beginning with any length and "cutting it" at the spot where the larger piece equals 1.618 times the smaller piece. Or looking at it from the point of view of the smaller piece, the smaller piece is .618 times the larger piece! It works out this way because the inverse of 1.618 equals .618, and vice-versa.
So the golden ratio is .618.... or 1.618 depending how you look at it (it seems to me). The negative solution is usually "discarded", even though its absolute value does equal .618, which is the golden ratio.