Research Project Phase I

8/2/2019 Research Project Phase I

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Sunni Singh

Golden Ratio

Research Project

Phase I


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What is the Golden Ratio.

The Golden Ratio, also known as phi is a geometric

relationship found in almost all of nature including the

human body, it is a number derived from Fibonacci'ssequence, if you pick two numbers that are in sequential

order on the sequence and divide the larger one by the

smaller one, almost always the number equals:

1.6180339887.... Some parts in the human body where

the golden ratio can be found are: the distance from the

eyes to the nose, in comparison with the distance from

your eyes to your chin. Another prime example is thelength of the first segment of the index finger which is the

tip to the first knuckle, compared with the second segment

of the index finger which is the first knuckle to the second.

(used this one in my analysis). Another one is length of the

hand, middle finger to wrist, compared with the length of

the forearm, wrist to elbow (also used in this analysis).

There is also the distance from the head to the naval, ascompared with your total height, amongst many more.

Tools Required To Collect Data.

The tools I required in order to collect the data included:

1x iPad 2


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1x. Measuring Tape

1x. TC-Stats by Professor Brian Jean

1x Pages by Apple Inc.

16x


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Data Collection Method.

The data collection consisted of going out and finding 16

people, 8 girls, and 8 guys, who were willing to participate,

and then proceed to collect the data I needed which

included the length of the first segment of the index finger

as well as the seconds segment of the index finger, the

length of the middle finger to the wrist, as well as the

length of the forearm, using the measuring tape. Thentaking this data and the IPad and inputting it into TC-Stats

properly.

Hypothesis.

I personally don't believe in the golden ratio, so I assumeit's not going to work, based on the information I disclosed,

you know that this could possibly be a biased view point,

but I will strictly stick to the data and try to be as neutral as

possible during this analysis.

Male Index Finger Data.

After collecting all the data, the result I got for the Male's

first segment Index Finger:


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From the above table we can infer that a total of 8 Malesubjects were tested (N=8). The total length of all their

fingers combined (Sum) is 18.65Centimeters, which

honestly isn't very useful information, but the Sample

Deviation will tell me that the average difference between

the 8 Males was only .21cm. The reason that the Sample

Deviation is so small is because the Subjects I used were

all around the same size and age. The mean of the 8subjects was 2.33cm, with the median being 2.30cm. The

difference between the max and the min is only .62cm

which I guess would actually be fairly large, when were

talking about such small numbers. Thats a difference of

about 25%.

The results I got for the second segment male's indexfinger:


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Again we know it was out of 8 Male subjects, the only big

difference in this information is the Sample Deviation is

larger which is expected because we are dealing with

larger numbers now. So nothing out of the ordinary here,the information matches up with what we would expect.

Results for Male Index Finger.

The above information doesn't tell us much about if it

follows the golden ratio unless we divide the first segmentby the second segment, which I was able to do, thanks to

the brilliant app called TC-Stats, and here is what I got:


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The row that is most important to us, is the very last one

the Golden Ratio is: 1.618 and those numbers are fairly

close to the Golden Ratio, lets take the mean of those

numbers and see how close we get:

Looking at the mean that is actually extremely close to the

golden ratio, There might be more truth to this golden ratio

thing then what I had originally hypothesized.


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Seeing how close the Male second index/Male first index

is we can tell that the standard deviation is really small,

and also slightly skewed right.

Female Index Finger Data.

The data for the Female's first segment index finger:

Information in this one, is not much different than the

Male's Data, the only thing that sticks out to me, other than

the fact that were dealing with smaller numbers is that the

sample deviation was just slightly smaller, I figured it

would be a little more smaller than it actually is, because

we were using smaller numbers. The Females I used arearound my age, just obviously not as tall.

Female's Second segment index finger:


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I was again surprised by the Sample Deviation again, by

the fact that it was actually bigger than the males, even

though we are working with smaller numbers, I wonder if Imade a collecting error possibly? But the numbers don't

seem to be to far out of the zone of realism, just slightly

higher than what I had projected.

Result for Female Index Finger.

Like I had stated in the male's results, the above

information doesn't do us much good, unless we compare

our results with the golden ratio, so when I divided the

larger segment by the smaller one, here is what I got:


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These numbers seem to vary too much, I think I could of

possibly made a mistake when collecting the data, lets

take the mean and see what we get:


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The mean is still fairly close, to the golden ratio, but it is

lower than the Male's mean but the sample deviation

seems to have skyrocketed compared to the Males, I can

only conclude that there was possibly a collecting error.

Here is a comparison of the two to help see the

differences in the Standard Deviation:


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See how much more spread the Female's second index/

first index is compared to the Mens? The rest of the data

seems to look okay though. Majority of the data seems

slightly skewed right.

Male Index finger to wrist.

Here is the data I got for the Male Index finger:

I used the same group of people as in the previous trials.The sample deviation seems to have grown, but that is

expected because we are dealing with larger numbers

now. Again this information will not tell us much other than

the average size, the smallest person used, and the

largest etc. not really crutial information to what we are

trying to prove or disprove.

Here is the data for the male wrist to elbow:


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Again, the Sample Deviation is getting larger because of

the larger numbers, nothing out of the ordinary here.

Male Wrist to Elbow Results.

Here are the results in relationship to the golden ratio:


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The numbers if we divide male wrist to elbow by the male

index to wrist is actually very close to the golden ratio.

Lets take the average and see what we find:

The average is actually still fairly close, and the standarddeviation is fairly small too, so the results seem pretty

strong.

Female Index to Wrist Data.

Here is the results that we got for the Female index towrist:

The standard Deviation is smaller than the males this time,

which is something I was hoping to get.


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Here is the Female's Wrist to elbow data:

In this data, very similar to the last, when compared to the

males, we have a smaller sample deviation as compared

to the Males.

Female index finger and elbow results.

here is the results as compared with the golden ratio:


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Were getting very consistent results around the golden

ratio, lets go ahead and take the average and see what we

get:


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The mean is actually really close to the golden ratio, and

the sample deviation is extremely small. We are still

getting numbers extremely close to the golden ratio.

here is the results for index to wrist to elbow of males and

females all compared:


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Here is a box and whisker plot of all the information

compared, the male wrist to elbow/ male index to wrist

compared with female index to elbow/ female index to

wrist, both of which are really close to the golden ratio.The numbers for males tends to be higher than females,

which would make since because most of the males in this

trial were taller than the females I used. Female index to

wrist seems slightly skewed right as well as the males

wrist to elbow.

In conclusion.

In conclusion I would say, that after all this testing I feel

like it is very plausible. I don't want to say anything truly

conclusive until I have done a lot more testing using a lot

more different people from different ethnicities, ages,sizes, etc. But I do believe that there might be something

here, as far as the golden ratio goes, numerous times,

during almost every trial, we got fairly close to the golden

ratio. Now if that is just coincidence or a testing error, or

real, I'm not really sure, unless I try to get the information

using different methods, with a different group of people, in

a completely different test.

Pictures.


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No project is complete without any pictures of the methods

used in the trials, so here are some pictures:


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Bibliography

http://en.wikipedia.org/wiki/Fibonacci_number. Fibonacci's

number. Accessed on February 25, 2012

http://faculty.taftcollege.edu/bjean/stat-1510/files/

researchproject.pdf. Research Project. Accessed on

February 20, 2012

http://en.wikipedia.org/wiki/Golden_ratio. Golden Ratio.

Accessed on February 28, 2012


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www.youtube.com%2Fwatch%3Fv%3D085KSyQVb-

U&ei=tzhdT7TWG-

iyiQLiobivCw&usg=AFQjCNHxwGtEoUYBPpueLwnxekMH

r-NwBA. Golden ratio in human body. Accessed March 1,2012

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Research Project Phase I