Difference between revisions of "Introduction" - Rhea

Revision as of 16:43, 2 December 2018

Introduction

File:Golden ratio.pdf

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 == Introduction ==
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-The golden ratio is a ratio such that, given two quantities a and b,
+[[File:Golden ratio.pdf|none]]
-(a+b)/a=a/b
-We can solve this equation to find an explicit quantity for the ratio.
-LHS=a/a+b/a=1+b/a
-+b/a=a/b
-We set the ratio equal to a certain quantity given by r.
-r≡a/b
-Then we can solve for the ratio numerically.
-+1/r=r
-r+1=r^2
-We can see from the above result that the golden ratio can also be described as a ratio such that in order to get the square of the ratio, you add one to the ratio.
-r^2-r-1=0
-We can then apply the quadratic formula to solve for the roots of the equation.
-r=(1±√(1^2-4(1)(-1) ))/2=(1±√5)/2
-The positive root is then the golden ratio.
-(1+√5)/2=1.618…≡ϕ
-The golden ratio, ϕ, is sometimes also called the golden mean or the golden section. The golden ratio can be frequently observed in man-made objects, though they are generally “imperfectly golden” – that is, the ratio is approximately the golden ratio, but not exactly. Some everyday examples include: credit cards, w/h=1.604, and laptop screens, w/h=1.602 (Tannenbaum 392).
-Visualizations of the golden ratio can be seen below (Weisstein):
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-[[2011_Fall_MA_265_Walther|Back to MA265 Fall 2011 Prof. Walther]]
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Difference between revisions of "Introduction" - Rhea

Revision as of 16:43, 2 December 2018

Introduction

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