Golden Ratio Phase One

8/2/2019 Golden Ratio Phase One

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Golden Ratio Project: Phase OneStats 1510 Day

Brian JeanBy: Briana Lemmons


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ABSTRACTUnder construction.INTRODUCTION The Golden Ratio, also known as Phi, or 1.618, is known to show up in manyplaces of our daily lives. Many people believe that nature is constructed with the Golden

Ratio, while others believe the Golden Ratio there by chance. The Golden Ratio can

easily be calculated by dividing two significant numbers. In this experiment, I decided to

calculate three different types of Golden Ratios that are found on humans. My first ratio

calculated was Total Height of the person divided by their Height from Foot to Belly

Button. My second ratio calculated was distance from Finger to Elbow divided by the

distance from the Wrist to Elbow. My third ratio calculated was the Length of Face

divided by the Width of Face. My hypothesis is that nature is, in fact, constructed with

the Golden Ratio. I hypothesize that my data I collect for each Golden Ratio will prove

this thought to be true. METHODS After conducting some research on the Golden Ratio, I decided to work withthree different ratios, as stated in the Introduction. My population of interest consists of

80 people, in which I broke down into groups. I separated the 80 people by Age,

Gender, and Ethnicity. There are two groups within each Age category: Male and

Female. In each of these Gender categories are Ethnic groups: Hispanic and White. :

Males and Females. Figure 1.1 shows the breakdown of the groups, and also identifies

the sample size of each group to make up the population of interest. Both Age groups


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h a v e a n e q u a l

amount of people

measured in the

group, so all people

selected to fit each

a g e g r o u p i s

representative of

that age group. In

Taft, Males make

up almost half of

the population, and

Females make up almost half of the population. Also, the ethnicities "Hispanic" and

"White" are dominant ethnicities in the town of Taft. Therefore, it's reasonable to assume

that each sample is representative of the population. After choosing a population size, I

went out and measured my population. Using a measuring tape, and calculating in

inches, I carefully measured each of the three ratios on each individual. I entered my

data into TC Stats and calculated each ratio in TC Stats. I then produced all of the

necessary graphs to display my data.

Figure 1.1


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RESULTS

AGE:

Figures 2.1 and 2.2 represent the Age category for Grade School (14yr - 18yr),with a sample size of 40, which includes both genders of both ethnicities. This box plot

gives us a lot of necessary information to answer our hypothesis. Looking at Figure 2.1

we see that Ratio #1 is bell shaped and seems to be the closest to the Golden Ratio.

Ratio #2 is skewed left and is shown to have data that is very spread out, which could

mean that it's far from the Golden Ratio. Ratio #3 is slightly skewed left and seems to

LEGENDRATIOS

Ratio #1 Total Height / Height from Foot to Belly Button.Ratio #2 Finger to Elbow / Wrist to Elbow.

Ratio #3 Length of Face / Width of Face.

Figure 2.1(Box Plot forGrade SchoolAges)

Figure 2.2 (Summary Statistics for Grade School Age Group)


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(RESULTS Contd.)have data just under the Golden Ratio. Figure 2.2, in many ways, is more valuable than

the box plot because it is easier for the human eye to understand since it is in chart form

and the numbers aren't displayed in graph form. Looking at the Summary Statistics in

Figure 2.2, we can conclude that Ratio #1 is the closest to the Golden Ratio, while Ratio

#2 is the farthest.

Figures 2.3 and 2.4 represent the Age category for College Age (19yr - 25yr),with a sample size of 40, which includes both genders of both ethnicities. Looking at

LEGENDRATIOS



Figure 2.3(Box Plot for College Age Group)

Figure 2.4 (Summary Statistics for College Age Group)


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(RESULTS Contd.)Figure 2.3 we see that looks very similar to figure 2.1. Looking at the box plot, Ratio #1

is bell shaped and seems to be the closest to the Golden Ratio. Ratio #2 is skewed left

and is shown to have data that is very spread out, which could mean that it's far from

the Golden Ratio. Ratio #3 is skewed right seems to have data just under the Golden

Ratio. Looking at the Summary Statistics in Figure 2.4, we can conclude that Ratio #1 is

the closest to the Golden Ratio, while Ratio #2 is the farthest.

GENDER:

LEGENDRATIOS



Figure 3.1(Box Plot Males)

Figure 3.2 (Summary Statistics for Males)


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(RESULTS Contd.) Figures 3.1 and 3.2 represent the Gender category for Males, with a samplesize of 40, which includes both ages and ethnicities. Figure 3.1 is different from what

we've seen so far in the box plot graphs. There is no data below 1. When we look at

Ratio #1 on the box plot, we notice it is bell shaped, and seems to be close to the

Golden Ratio. Ratio #2 is skewed right and seems to have data just under the Golden

Ratio. Ratio #3 is skewed left and is difficult to judge if it's close to the Golden Ratio or

not. Looking at the Summary Statistics in Figure 3.2, we can conclude that Ratio #1 is

the closest to the Golden Ratio, while Ratio #3 is the farthest.

LEGENDRATIOS



Figure 3.3 (Box Plot Females)

Figure 3.4 (Summary Statistics for Females)


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(RESULTS Contd.) Figures 3.3 and 3.4 represent the Gender category for Females, with a samplesize of 40, which includes both ages and ethnicities. When we look at the box plot, we

notice Ratio #1 is bell shaped, and seems to be close to the Golden Ratio. Ratio #2 is

skewed left and seems to have data right around the Golden Ratio. When we look at

Ratio #3 on the box plot, we notice that the mean and the 3rd Quartile are the same.

We also notice that Ratio #3 is skewed right and is difficult to judge if it's close to the

Golden Ratio or not. Looking at the Summary Statistics in Figure 3.4, we can conclude

that Ratio #1 is the closest to the Golden Ratio, while Ratio #3 is the farthest.ETHNICITY:

LEGENDRATIOS



Figure 4.1 Box Plot(Hispanic)

Figure 4.2 (Summary Statistics for Hispanic)


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(RESULTS Contd.) Figures 4.1 and 4.2 represent the Ethnicity category for Hispanic ethnicities,with a sample size of 40, which includes both ages and genders. When we look at Ratio

#1 on the box plot, we notice that Ratio #1 is bell shaped, and seems to be close to the

Golden Ratio. Ratio #2 is skewed left and seems to have data right around the Golden

Ratio. Ratio #3 is skewed right and looks like the data might be right under the Golden

Ratio. Looking at the Summary Statistics in Figure 4.2, we can conclude that Ratio #1

is the closest to the Golden Ratio, while Ratio #3 is the farthest.

LEGENDRATIOS



Figure 4.3Box Plot(White)

Figure 4.4 (Summary Statistics for White)


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(RESULTS Contd.) Figures 4.3 and 4.4 represent the Ethnicity category for White ethnicities, with asample size of 40, which includes both ages and genders. When we look at Ratio #1 on

the box plot, we notice that Ratio #1 is bell shaped, and seems to be close to the

Golden Ratio. Ratio #2 is skewed left and seems to have data right above the Golden

Ratio. Ratio #3 is bell shaped and the data is hard to determine. Looking at the

Summary Statistics in Figure 4.4, we can conclude that Ratio #2 is the closest to the

Golden Ratio, while Ratio #3 is the farthest.

BibliographyAngie Greek (2007, November 23). The Golden Mean. Retrieved February 15, 2012from http://youtu.be/2zWivbG0RIoBiziarek (2007, May 11). The Fingerprint of God. Retrieved February 21, 2012 fromhttp://youtu.be/-Ibc8sD5sgwBricke321 (2008, September 25). Golden Ratio. Retrieved February 12, 2012 from

http://youtu.be/fmaVqkR0ZXgHigh Flying Dutchman (2008, September 18). Golden Ratio in Human Body. RetrievedFebruary 17, 2012, from http://youtu.be/085KSyQVb-UKahn Academy (2011, October 5). The Golden Ratio. Retrieved February 12, 2012, fromhttp://youtu.be/5zosU6XTgSYScience Vs. Evolution (2010, May 10). The golden ratio in the human face. RetrievedFebruary 17, 2012 from http://youtu.be/Wy6cqVUloJQYaratilistr (2010, March 28). Golden Ratio in Human Body 1.618. Retrieved February09, 2012 from http://youtu.be/PNQk_GJuZQo


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AppendixLEGEND

RATIOS



AGES

College

(19 yr - 25 yr)

Notation: C

Gradeschool(14yr - 18yr)

Notation: G

GENDER

Male Notation: MFemale Notation: F

ETHNICITY

Hispanic Notation: H

White Notation: W

Age Gender Ethnicity Ratio #1 Ratio #2 Ratio #3

C M H 1.65 1.65 1.7

C M H 1.6098 1.65 1.4

C M H 1.5 1.7391 1.4545

C M H 1.5955 1.7619 1.4167

C M H 1.6279 1.7619 1.4167

C M H 1.5854 1.5909 1.6

C M H 1.622 1.4783 1.4545

C M H 1.5854 1.5238 1.4

C M H 1.4583 1.6364 1.6

C M H 1.5778 1.7143 1.3333

C M W 1.5632 1.4783 1.4545

C M W 1.6322 1.619 1.4

C M W 1.6429 1.6818 1.6

C M W 1.6591 1.6364 1.4545

C M W 1.5862 1.5909 1.2727

C M W 1.5341 1.6522 1.0769

C M W 1.6222 1.625 1.6

C M W 1.5579 1.5833 1.5455

C M W 1.5455 1.7895 1.4

C M W 1.5778 1.6818 1.4545

C F H 1.5844 1.7647 1.4

C F H 1.6341 0.641 1.2727

C F H 1.6047 1.7895 1.4

C F H 1.5949 1.65 1.3

C F H 1.6 1.6364 1.4


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(Appendix Contd.)LEGEND

RATIOS



AGES

College

(19 yr - 25 yr)

Notation: C

Gradeschool(14yr - 18yr)

Notation: G

GENDER

Male Notation: MFemale Notation: F

ETHNICITY


White Notation: W


C F H 1.575 1.7 1.2727

C F H 1.5366 1.65 1.4

C F H 1.6154 1.5238 1.4

C F H 1.6 1.619 1.2727

C F H 1.5949 1.65 1.4

C F W 1.725 1.6667 1.7778

C F W 1.6 1.6842 1.3636

C F W 1.6 1.3043 1.2727

C F W 1.5682 1.75 1.2727

C F W 1.6098 1.7222 1.2727

C F W 1.5581 1.75 1.3

C F W 1.6 1.7 1.4

C F W 1.6279 1.5652 1.7

C F W 1.561 1.2188 1.2727

C F W 1.575 1.2174 1.2727

G M H 1.675 1.7 1.5455

G M H 1.7105 1.7368 1.6

G M H 1.561 1.7143 1.3333

G M H 1.5455 2 1.7

G M H 1.625 1.7368 1.4545

G M H 1.6429 1.7895 1.2727

G M H 1.6047 1.75 1.4167

G M H 1.5854 1.75 1.6

G M H 1.625 1.8421 1.4545

G M H 1.622 1.5909 1.4545


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(Appendix Contd.)LEGEND

RATIOS



AGES

College

(19 yr - 25 yr)Notation: C

Gradeschool

(14yr - 18yr)Notation: G

GENDERMale Notation: M

Female Notation: F

ETHNICITY


White Notation: W


G M W 1.5778 1.6522 1.5455

G M W 1.6591 1.7143 1.4545

G M W 1.587 1.7143 1.7

G M W 1.5435 1.6818 1.6

G M W 1.6 1.8261 1.0769G M W 1.5455 1.7895 1.5

G M W 1.6222 1.625 1.6

G M W 1.5227 1.6364 1.0769

G M W 1.6136 1.7143 1.6

G M W 1.5745 1.6522 1.7

G F H 1.619 1.65 1.4

G F H 1.5802 1.6667 1.2727

G F H 1.6341 1.7895 1.1667

G F H 1.6125 1.8333 1.4

G F H 1.6154 1.7778 1.5

G F H 1.5952 1.5909 1.4

G F H 1.5952 1.75 1.1818G F H 1.5814 1.75 1.5

G F H 1.6154 1.7 1.1818

G F H 1.5227 1.6087 1.3

G F W 1.6092 1.6522 1.5

G F W 1.6279 1.6364 1.6

G F W 1.5897 1.7647 1.4

G F W 1.675 1.6842 1.5556

G F W 1.6154 1.6 1.4

G F W 1.4432 1.8 1.2727

G F W 1.625 0.7179 1.6667

G F W 1.6 1.7 1.4

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Golden Ratio Phase One