The Golden Ratio

The well-heeled symmetry is approximately 1.6. The mysteriously aesthetic all(prenominal)y winning balance is the relation ?a+b is to a as a is to b? or a+b/b=a/b=?. It is denoted as the Greek letter ? or ? (lower case, upper case respectively, upper case most a lot used as reciprocal). The letter is pronounced ?phi?. The golden symmetry is put in with child(p)ly in art, nature, and architecture. Through out the centuries unfathomable mathematicians harbor spent countless hours with the golden ratio and all its applications. It go off be found in the striking pyramid of Giza, the Parthenon and the Mona Lisa. It is prominent in human and animal anatomy, it foot be found in the structure of plants, and even the desoxyribonucleic acid molecule exemplifies the ratio 1.6. The golden ratio also has applications in other mathematical comparisons such as logarithmic spirals and the Fibonacci numbers. to begin with we give the sack bring to discuss the application o f the golden ratio we must stress how we translate ?a+b is to a as a is to b? into the real, usable number 1.6. Phi is an blind number, so it?s impossible to calculate exactly, but we provoke calculate a close approximation. As preceding(prenominal)ly stated, the basic equate for phi is a+b/a=a/b=?. So if a/b=?, then a=b?. straight off returning to our previous equating, a+b/a=?, we can put back a for b?. After change we have b?+b/b?=b?/b. Dividing out by b gives us ?+1/?=?.

Rearranging yields the quadratic equation ?2-?-1=0. Therefore via previous knowledge of the general form of a quadratic equation (ax2+bx+c=0) we can ext rapolate the following(a) values for our ph! i equation: a=1, b=-1, c=-1. change these numbers in the quadratic function: x=[-b+/-?(b2-4ac)]/2a and you come ?=[1+/-?5]/2. This allows us to remember the roots of the equation; ?=1.618 033 989 (commonly stated 1.6) and ?=-0.618 033 989 (??? connect to Fibonacci numbers). If you want to get a full essay, order it on our website: BestEssayCheap.com

If you want to get a full essay, visit our page: cheap essay