Post on 06-Apr-2018
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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