Archive for February 11th, 2011

February 11, 2011

Golden Ratio

golden ratio

If a person has one number a and another smaller number b, he can make the ratio of the two numbers by dividing them. Their ratio is a/b. He can make another ratio by adding the two numbers together a+b and dividing this by the larger number a. The new ratio is (a+b)/a. If these two ratios are equal to the same number, then that number is called the golden ratio. The Greek letter \varphi (phi) is usually used to represent the golden ratio. Like Pi, the golden ratio is an irrational number. If a person tries to write it, it will never stop and never be the same again and again, but it will start this way: 1.6180339887…

Italian mathematician, Fibonacci (1170 – 1250), discovered a sequence of numbers that relates to the golden ratio called the Fibonacci numbers.  A person can find the next number in the list by adding the last two numbers together. If a person divides a number in the list by the number that came before it, this ratio comes closer and closer to the golden ratio. At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties.