Difference between revisions of "Introduction" - Rhea

Latest revision as of 15:53, 2 December 2018

Introduction

In this paper, we are going to discuss the logistic model of predicting the population and its historical applications on the size of US population. Population of the United States is the total number of people living in the United States with US citizenship. Population projection is the estimation of the future size of the population. Section II will mention the official source and relating background about the size of US population. Section III will address why population projection is important. Section IV will briefly go over exponential population model which had great influence on the invention of logistic population model. Section V will focus on logistic model and its derivations. Section VI will discuss some historical application of logistic model. Section VII includes citations.

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-[[File:Golden ratio.pdf|thumbnail]]
-[[Category:honors project]]
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 == Introduction ==
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+In this paper, we are going to discuss the logistic model of predicting the population and its historical applications on the size of US population. Population of the United States is the total number of people living in the United States with US citizenship. Population projection is the estimation of the future size of the population. Section II will mention the official source and relating background about the size of US population. Section III will address why population projection is important. Section IV will briefly go over exponential population model which had great influence on the invention of logistic population model. Section V will focus on logistic model and its derivations. Section VI will discuss some historical application of logistic model. Section VII includes citations.
-The golden ratio is a ratio such that, given two quantities a and b,
-(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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Difference between revisions of "Introduction" - Rhea

Latest revision as of 15:53, 2 December 2018

Introduction

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