I came to this question just recently, when I discovered how to calculate the value of φ (phi). I found out this equation:
(a+b)/a=a/b=φ ; where a is the larger part, b is the smaller part, and a+b is the combination of the two.
Working with the equation a/b=φ, a=bφ.
Substituting bφ to a in the equation (a+b)/a=a/b, it will become:
(bφ+b)/bφ=bφ/b
[b(φ+1)]/bφ=φ
(φ+1)/φ=φ
φ+1=φ^2
φ^2-φ-1=0
Solvin this equation using the quadratic formula, φ is equal to:
φ = {1 + [5^(1/2)]}/2
with this, φ is approximately 1.618
With this solution, compared to the solution for the value of π, this is more concise and short. Actually, this is a LOT shorter.
Considering that both π and φ ARE irrational, and the value for φ can be computed as shown above, is there a shorter way to compute for the value of π?
I'm just so curious...
2006-08-12
23:47:23
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11 answers
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fictitiousness ;-)
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Mathematics