phi is incorperated into the golden rectangle, because if you divide the longer side of the golden rectangle by the shorter sid, the answer will be phi.(1.168...)
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ϕ (PHI)
In math, Phi, or the Golden ratio is approximatly 1.6180339887.Otherwise, Phi is how you pronounce a greek letter.
The Golden Rectangle was believed to be founded by Pythagoras. The Golden Rectangle was used for many Greek Buildings such as the Parthenon, and the Villa Stein.
The golden ratio, or golden mean, or phi, is about 1.618033989. The golden ratio is the ratio of two quantities such that the ratio of the sum to the larger is the same as the ratio of the larger to the smaller. If the two quantities are a and b, their ratio is golden if a > b and (a+b)/a = a/b. This ratio is known as phi, with a value of about 1.618033989. Exactly, the ratio is (1 + square root(5))/2.
The golden ratio (or Phi) is a ratio that is very commonly found in nature. For instance, some seashells follow a spiraling path at the golden ratio.
1 to phi
The golden number? Phi = 1.61803398872...
when golden rectangle constructed?
Suppose you have a rectangle with long side (length) a and short side (breadth) b. Put it next to a square of sides a. This will make a rectangle with length a+b and breadth b.The rectabgles have sides in the Golden Ratio if(a + b)/a = a/b = phi.If you substitute b = 1 in the above ratio, you get phi as the root of a^2 - a - 1 = 0so that phi = [1 +/- sqrt(5)]/2 = 1.6180, approx, {and -0.6180}.
Phi Sigma Epsilon's motto is 'Golden Rule'.
phi = [(1+sqrt(5)]/2 = 1.6180, the golden ratio. cosine(phi) = -0.0472 approx.
ϕ (PHI)
Euclid was the one to construct the golden rectangle
A golden rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1:1.618. A 3x5 card has side lengths of 3 inches by 5 inches, which do not match the golden ratio. Therefore, a 3x5 card is not a golden rectangle.
In math, Phi, or the Golden ratio is approximatly 1.6180339887.Otherwise, Phi is how you pronounce a greek letter.
(a+b)/a=a/b=phi (the golden ratio, as defined) (a+b)/a=phi (we'll solve this equation) 1+b/a=phi (just changing the form of the left side a little) 1+1/phi=phi (a/b=phi so b/a=1/phi) phi+1=phi2 (multiply both sides by phi) phi2-phi-1=0 (rearrange) From here, we can use the quadratic equation to find the positive solution: phi=(-b+√(b2-4ac))/(2a) phi=(1+√(1+4))/2 phi=(1+√5)/2≈1.618
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