Golden Ratio Stats

8/2/2019 Golden Ratio Stats

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Mateo Solano

The Golden Ratio & the Human Body

Stats 1510 Night


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Introduction

The Golden Ratio is a number that seems to appear everywhere in nature so much so

that it has also been called the Divine Proportion because many believe that this

number is all by which nature is governed. It is based on the Fibonacci numbers. These

are a series of numbers that begin with 0 and 1 after that you follow the rule of adding

the last two numbers to get the next 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610,

987,... and so on. "A special value, closely related to the Fibonacci series, is called the

golden section; this value is obtained by taking the ratio of successive terms in the

Fibonacci series"(1). The Golden Section is yet another name for the Golden Ratio.

The Golden Ratio is denoted by the Greek symbol Phi and can be determined when

the measurement of A is added to the measurement of B and divided by the

measurement of A giving you (A + B)/A. Phi is equal to approximately 1.61803399.

"The Golden Section, also known as Phi, is manifested in the structure of the human

body. If the length of the hand has the value of 1, for instance, then the combined length

of hand + forearm has the approximate value of Phi." (2) Similarly the proportion of

navel to top of head to + shoulder line to top of head is in the same ratio of 1: Phi .The

purpose of this research project was to determine if in fact these measurements would

result in the ratio of 1:Phi or the Golden Ratio. The measurements were taken from two

populations the first was adult males over the age of 18 and the second was adult

females over the age of 18. In collecting the data 40 males and 40 females for a total of

80 subjects were measured for the length in inches from the above mentioned areas to

establish the two ratios and determine whether those ratios were in fact calculated to be

the Golden Ratio. These two sets of data were then compared to each other.


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Methods and Materials

In collecting the data 40 random males and 40 random females were approached in

various locations and asked if they wouldn't mind being measured from their fingertips

to the their elbows from their wrist to their elbows and from their shoulder line to the top

of their heads and from their navels to the top of their heads. Each subject was

measured using a five foot body measuring tape. The results were recorded on paper

and transferred into tcstats on an ipad.

Results

Neither the males nor the female measurements when calculated using the formula (A +

B)/A resulted in the Golden Ratio and although the mean for both male and female ratio

# 2 did produce a number close to Phi it was in fact not Phi. Tables 1.1 and 2.1 list the

five number summary for each ratio both female and male respectively along with the

population standard deviation and sample standard deviation, as well as the sum of all

the data for the sample which was equivalent to 40 males and 40 females or n = 40; n

being the sample size. Tables 1.2 and 2.2 list the five number summary of female and

male respectively for each of the measurements, along with the population standard

deviation and sample standard deviation, as well as the sum of all the data for the

sample which was equivalent to 40 males and 40 females or n = 40; n being the sample

size. The five number summary consists of the minimum data value for each ratio, the

Q1 value, such that no more than 25% of all values are smaller and no more than 75%

are larger, the mean which is the average and the number that represents the center


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point of the data, the Q3 value, such that no more than 75% of all values are smaller

and no more than 25% are larger, and finally the maximum value of the data set. As

you can see from reading table 1.1 the average for female ratio #1 was 1.415585 which

represented the mean of the sum of the measurements from the shoulder line to the top

of the head and the navel to the top of the head divided by the length of measurement

from the navel to the top of the head. This number was not the Golden Ratio. The

same calculation was used to calculate female ratio #2 which was the sum of the

measurements from the middle fingertip to the elbow and the wrist to the elbow divided

by the length of measurement from the middle finger to the elbow; and as can be read

in Table 1.1 the average of the this data set came out to be 1.613727 which again

comes close to the numerical value of Phi but is not the Golden Ratio itself.

In this research age was not taken into consideration other than the fact that the

subjects were considered to be adults if over the age of 18. The only place where the

data might have been affected from this would be in the female measurements from the

navel to the top of the head as there was a deviation of over one and a half inches.

Although even with this deviation the deviation in ratio #1 was very small, the sample

standard deviation being 0.03082269. Likewise the deviation in ratio #2 was also very

small, 0.0340273.

The same holds true for the male data listed in Tables 2.1 and 2.2. The standard

deviation was more than one and a half inches (1.713) from the navel to the top of the

head but the overall deviation for the ratio was very small (0.03323601). The male data

also when input into the calculation for the Golden Ratio failed to produce Phi as the


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result. Also just as in the female data the mean for ratio #2 was numerically close to the

Golden Ratio but was in fact not Phi. All of the figures for the male data can be seen in

Tables 2.1 and 2.2

A visual representation of the data can be seen in figures 1.1 for and 1.2 for both of the

female ratios and 2.1 and 2.3 for the male ratios. Both sets of box and whisker plots

show the distribution of data to be symmetrical. The graphs are based on the data from

Tables 1.1 and 2.1 for the female and male five number summaries respectively.

Table 1.1

Table 2.1


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Table 1.2

Table 2.2

Figure 1.1


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Figure 2.1


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Appendix


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Head to Shoulder

Line

Navel to top of

Head

Female Ratio

#1

Finger to

Elbow

Wrist to

Elbow

Female Ratio

2

10.5 26 1.44 17.5 11.5 1.6

10 25.5 1.3922 16.5 10 1.6

11.5 27 1.4259 17 10.5 1.6

11 30.5 1.3607 17.5 10 1.511 26 1.4231 17 11 1.6

12 27.5 1.4364 17.5 11 1.6

11 25 1.44 17.5 11 1.6

10.5 24 1.4375 16.5 10.5 1.6

10 25.5 1.3922 17 11.5 1.6

11 26 1.4231 17.5 10 1.5

11 27 1.4074 15 9

10 26 1.3846 16 10.5 1.6

12 27 1.4444 18 10.5 1.5

11 23 1.4783 15 8.5 1.59.5 25 1.38 16 9 1.5

10 25 1.4 14.5 9 1.6

10 24.5 1.4082 16.5 10.5 1.6

11 29 1.3793 15.5 9 1.5

11 28 1.3929 16.5 10 1.6

11.5 25 1.46 15.5 9 1.5

10.5 25.5 1.4118 14.5 9.5 1.6

11 25 1.44 14.5 9 1.6

10.5 27 1.3889 17.5 11 1.6

11.5 28.5 1.4035 17 10.5 1.6

11.5 27 1.4259 16.5 10.5 1.6

10.5 27 1.3889 17 11 1.6

10.5 23 1.4565 16 9.5 1.5

9 27 1.3333 15 10 1.6

10.5 24 1.4375 16 10 1.

10 25 1.4 16.5 9 1.5

11 25 1.44 16 9.5 1.5

11.5 25.5 1.451 16.5 10 1.6

10 22.5 1.4444 16 9.5 1.5

10 25 1.4 16 10 1.

11 25 1.44 16 9 1.5

10 24.5 1.4082 16 9 1.5

9.5 26.5 1.3585 18 10.5 1.5

10 24 1.4167 18 11.5 1.6

11 24.5 1.449 16 10.5 1.6

11 26 1.4231 16.5 10 1.6

Adult female data


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Navel to

Head

Head to Shoulder

Line

Male Ratio

#1

Finger to

Elbow

Wrist to

Elbow

Male Ratio

#2

24 9 1.375 17.5 10.5 1.6

25 10 1.4 17 10.5 1.6176

27 11 1.4074 18 10.5 1.5833

28.5 11 1.386 17 9.5 1.558829 9 1.3103 18 11.5 1.6389

26 10 1.3846 16.5 10 1.6061

27 11 1.4074 18 11 1.6111

27 11 1.4074 17 9.5 1.5588

26.5 11.5 1.434 17.5 10.5 1.6

27 12 1.4444 18.5 11 1.5946

24 11 1.4583 18.5 11.5 1.6216

26.5 12 1.4528 18 10 1.5556

25.5 10.5 1.4118 16.5 9.5 1.5758

26 11.5 1.4423 17.5 10 1.571425 11 1.44 15.5 11 1.7097

24 11 1.4583 17 10 1.5882

26 11 1.4231 18.5 11 1.5946

28 10 1.3571 18 11 1.6111

27 11 1.4074 18 11 1.6111

26.5 11 1.4151 18.5 12 1.6486

25 11.5 1.451 17 11 1.6471

28 12 1.4286 17 10.5 1.6176

27.5 10.5 1.3818 16 10 1.625

26.5 10.5 1.3962 17 10 1.5882

26.5 11 1.4151 20 11.5 1.575

25.5 11 1.4314 17 11 1.6471

25 10 1.4 18.5 10.5 1.5676

28 12 1.4286 18.5 10 1.5405

28 12 1.4286 19 11 1.5789

30 12 1.4 18 11.5 1.6389

28 11 1.3929 18 12 1.6667

27.5 11 1.4 18.5 11 1.5946

30 10.5 1.35 17 11.5 1.6765

23.5 11 1.4681 19 12 1.6316

26.5 10.5 1.3559 18.5 10 1.5405

27.5 11.5 1.4182 18.5 10.5 1.5676

29 12.5 1.431 17 10.5 1.6176

28.5 11 1.386 18.5 10.5 1.5676

28.5 11 1.386 17 10 1.5882

30.5 11.5 1.377 19.5 12.5 1.641

Adult male data

Golden Ratio Stats

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