Can Someone Please Explain This Equation?

Darth BeaverDarth Beaver Meine Ehre heißt Treue
edited December 2011 in Tech & Games
Can one of you math geeks err geniuses please explain what this really means in English?

1: φ + 1 = φ²

and

2: φ - 1 = 1/φ

All I see when I looked at this is the following:

1: Some value (supposedly the golden number φ, WETF that is) plus one equals the same value squared. So how can you take a value, add one, and it be equal to that same value times itself?

2. Some value (again with this mysterious golden number φ) minus one equals one divided by this same value. So how can you take a value, subtract one, and it be equal to one divided by that same value?

What, in English, is this golden number (φ) and why does it defy mathematical logic/principles? I mean if I take any whole number and add one it does not and can not equal itself squared. Or if I take any whole number and subtract one it does not and can not equal one divided by itself. So can one of you explain in simple English what this golden number (φ) is and how these equations are possible using it?

Comments

  • chippychippy <b style="color:pink;">Global Moderator</b>
    edited December 2011
    Two quantities a and b are said to be in the golden ratio φ if:
    .26aac0b3f0b9b167de1bc16d619472c0.png
    One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ,
    ,34f9cdbdc7cf831a545673bc94c8eea9.png
    it is shown that,
    b0b7b7cf91f69a10a4982056c3ad0b50.png
    Multiplying by φ gives
    φ + 1 = φ2
    which can be rearranged to
    φ2 − φ − 1 = 0.
    Using the quadratic formula gives the only positive solution as,
    .95bc36564d7881ed482ec63057533f2d.png
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