How to Calculate Phi
- 1). Call the length of your unbroken line 1 unit. Section it at point x, dividing your line into a larger section, x units long, and a smaller section, 1-x. The ratio of the whole line to the larger segment, 1 / x = the ratio of the larger segment to the smaller segment, x / (x-1).
- 2). Multiply both sides of this equation by x to get: 1 = x^2 / (1-x).
- 3). Multiply both sides by 1-x to get : 1 - x = x^2. Rearrange this to get: x^2 +x-1 =0
- 4). Use the quadratic equation to solve for x to get x =(√5-1)/2. Phi is the ratio of 1 over x. Because x is a fraction, you can simply flip the numerator and the denominator to determine the value of 1 over x. Phi = 2/(√5-1)
- 5). Multiply both top and bottom by (√5+1). The numerator becomes 2(√5+1). The denominator becomes (√5-1)(√5+1). Using FOIL (First, Outer, Inner, Last) method to multiply, you'll get 5 +√5 -√5 -1. That works out to 5-1, which is 4.
- 6). Divide numerator and denominator by 2: 2(√5+1) /4 = (√5+1)/2. You have calculated Phi.
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