Tony (Anthony) Hanmer wrote:
The Golden Ratio, also known as the Greek letter phi (pronounced "fee") and several other names, is indeed a fascinating number. It is approximately 1.1680339887499; or is it this number minus 1? Anyway, it is the only answer to the question, Which number satisfies *both* 1/x = x-1 and x^2 = x+1?... Wild. It is also calcualted as ((sqrt 5)-1)/2. It appears in numerous surprising places in nature as well, such as angles of packing of sunflower seeds and ratios of flower petals in many species.
"*both* 1/x = x-1 and x^2 = x+1?... Wild." these are the same formula and both come from x^2 -x -1 =0 the roots of this polynomial are -b +- sqrt(b^2 -4ac) /(2a) quadratic formula which gives "It is also calcualted as ((sqrt 5)-1)/2." So it is all just one formula wrtten 3 different ways. Doug Stewart