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The Golden Ratio "Beauty"

Science Summative

Alison Lieu

on 23 May 2014

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Transcript of The Golden Ratio "Beauty"

The Golden Ratio "Beauty"
Rachel Dratch
Beyonce Knowles
Angelina Jolie
The Marquardt Beauty Mask
Golden Ratio Results
Eighteen volunteers were asked to fill out the following survey:

Rate the following celebrities on a scale of 1-10 (judge only based on their facial features) *10=most attractive

1) Rachel Dratch
2) Angelina Jolie
3) Beyonce Knowles
4) Shania Twain
5) Brad Pitt
6) Drake Graham
7) Leonardo Di Caprio
8) Kanye West

The desirability score was obtained by finding the average of the scores. The celebrity with the highest score was Angelina Jolie with the score of 8.17. The celebrity with the lowest score was Rachel Dratch with a desirability score of 3.6.
Survey Results
To calculate the facial measurements relative to the golden ratio, the following ratios were used: A/G, B/D, I/J, I/C, E/L, F/H, K,E. The perfect face according to the golden ratio would have each of the ratios above to have the value of 1.618.

(A) Top of the head to the chin
(B) Top of the head to the pupil
(C) Pupil to nose tip
(D) Pupil to the lip
(E) Width of the nose
(F) Outside distance between the eyes
(G) Width of the head
(H) Hairline to the pupil
(I) Tip of the nose to the chin
(J) Lips to the chin
(K) Length of the lips
(L) Tip of the nose to the lips
The purpose of this experiment was to see whether there was a correlation between the golden ratio and the perception of one's attractiveness.

To improve the investigation, I should have used volunteers pertaining to a wider range of ages since age is a major factor that affects one's perception. Having a larger amount of participants could have increased the accuracy of this experiment as trends are often more accurate and easier to detect when there is a high amount of participants. I should have also used the faces of unknown people, instead of using celebrities, due to the recognizability of the celebrities to the participants. People may have had previous exposure to these celebrities which may have biased their results when asked to provide a desirability score for the celebrities.

I could have also used an electronic program like Photoshop to conduct my measurements as measuring the faces by hand could produce results that are not as precise.

I should have chosen people with a wider range of variance from the golden ratio since 5 of my 7 chosen celebrities had a variance between 0.2-0.29, with the remaining two celebrites being very close or very far from the ratio.

Taking in account these measures if one was to conduct a similar or the same experiment would likely improve accuracy.

I hypothesize that celebrities with a smaller diversion from the golden ratio average will be perceived as more attractive. Therefore as the diversion average increases, one will be perceived to be less attractive.

Find images of celebrities that you find to be unattractive and attractive. The images need to be of a clear image of the face and need to be relatively the same size.

2) Print out the images in colour to allow for a more realistic and clear comparison to the real person.

3) Measure the specific measurements listed using a ruler and record the measurements (round the measurements to the nearest tenth of a decimal).

4) Using the results from above, divide the measurements according to the ratios listed to find the measurements in comparison to the golden ratio.

5) Create a survey with images of each of your chosen celebrities on it and asking the question: How attractive would you rate this person, on a scale of 1-10? *10 is the most attractive.

6) Find 18 volunteers (random) that are diverse to fill out your survey.

7) Evaluate your results from the survey and evaluate your results from your measurements.

8) Graph your results. If applicable, graph the data you want to see have correlation with each other or not on the same graph

9) Conduct additional research on the topic of the golden ratio to allow for a more accurate conclusion

10) Write your conclusion based on your collected data, your graphs, and your additional research.

*"measurements listed" and "ratios listed" are found on the "Golden Ratio Results Slide"

This experiment investigates the relationship between the Golden Ratio and the perception of beauty. The perception of beauty has always been deemed very subjective and varying from person to person. Having said that, there has been the ideology that "perfect beauty" can be achieved if one's facial measurements were correlated to the golden ratio. The results from similar experiments have been inconclusive. Nevertheless, I conducted this experiment to see if I could gather results that supported the correlation. I thought it would be interesting to see if the golden ratio, which involves mathematics, can help explain our perception of attractiveness.
Shania Twain
Brad Pitt

Drake Graham
Leonardo DiCaprio
Kanye West
- printer






-18 volunteers (random)
What is the Golden Ratio? .

It is also known as divine proportion. It is noted as phi and has a value that is approximately 1.618. The golden ratio is an irrational number as it has digits that go further than 1.618. You can find the golden ratio of any number by dividing 1 by your chosen number and then adding 1 to that quotient. The concept of the golden ratio is that if there are two distances, one that is larger and one that is smaller, and you divide the larger distance by the smaller distance, it is equal to the entire distance divided by the larger distance. Therefore if there are two measurements that fit the description above, the ratios should both be about 1.618, and the measurements would be considered as golden.

Why is it used?

Many people believe that objects that have these golden measurements make the object seem more attractive or more pleasing to the eye although there is currently not enough evidence to prove this belief is factual. Nevertheless, the golden ratio is used by many and is found in many objects. Numerous famous artists like Leonardo Da Vinci have used this golden ratio in many of their works. The most famous example is the painting of Mona Lisa; Leonardo constructed her face according to the golden ratio. Most Renaissance artists used this ratio due to the importance of the concepts of perfection and precision of that time. There is also a lot of architecture that has been built with this ratio in mind such as ancient and modern architectural structures (the Pyramids, the Parthenon and the CN Tower). There are also things found in nature that have measurements very close to this ratio, some of which include human faces and human bodies. This experiment, like many conducted, will attempt to see if the golden ratio affects one’s perception of beauty.


What influences visual perception?

The perception of anything is scientifically formed with your brain and nervous system, but many factors influence one’s visual perception. As every individual is different, defining a reason as to why certain people perceive something a certain way is therefore never conclusive. One of the factors that affects one’s perception is one’s culture. The traditions and customs that one is brought up in affects one’s mental development, which subsequently affects the way one perceives things. There have also been studies that have shown that imagery might influence perception. Envisioning something in one’s mind is said to influence how the real object/person would be perceived in real life.


Other factors that would affect one's visual perception would include gender, age, and visual impairment. Factors that can be controlled by humans may include the lighting and angle/point of viewing of the subject. Previous exposure or interactions with the subject will likely affect the way the object is perceived. For example, if one is asked to judge the attractiveness of her favourite actor, the participant may produce bias results depending her previous opinions on the male.

Studies have shown that one finds things with symmetry and proportion to be more pleasing to the eye. Therefore, the human face is no exception. There has also been studies conducted that show that people find the average face more attractive than faces that are below or above average.
My findings are significant because it shows that there is no concrete correlation between one's attractiveness and their facial measurements relative to the golden ratio. This is important since there has been a lot of discussion regarding the use of this ratio to achieve maximum beauty and applying this ratio in plastic surgery and other measures. Based on my findings and similar findings from others that have conducted a similar experiment, it will hopefully inform those that are not aware that there is no concrete evidence to support a strong correlation between the two things.
Diversion from the Golden Ratio (1.618)
Of the celebrities measured, the celebrity with the smallest average diversion from the golden ratio is Shania Twain. Therefore, her face is the closest to the perfect face according to the golden ratio. Drake Graham has the highest diversion from the golden ratio, therefore his face is the furthest from the perfect face.
Works Cited
Angelina Jolie Pics 2014. mosta2bal. 2014. Online Photograph. Web. 17 May. 2014.

Doyle, Megan. Investigating Beauty with the Golden Ratio.Education.com. 2014.

Web. 28 Apr. 2014.

Goodstein, Shelley. The Perfect Face-Golden Ratio Beauty Calculator. A model’s

secrets. 16 Jan. 2012. Web. 10 May. 2014.

Bourne, M. The Math Behind the Beauty. Interactive mathematics. 21 May. 2014.

Britton, Jill. Golden Section in Art and Architecture.06 May. 2012. Web. 06 May. 2014.

Drake Graham. Daily Mail. 09 Jan. 2012. Online Photograph. Web. 18 May. 2014.

Leonardo Di Caprio.idposter.com. May. 2013.Online Photograph. Web. 13 May. 2014.

Kanye West. The Mater Copy. July. 2013. Online Photograph. Web. 13 May. 2014.

Meisner, Gary. Human Beauty and the Golden Ratio. 12 Jan. 2014. Web. 10 May. 2014.

The Beauty Equation. Oprah. 14 Aug. 2009. Web. 11 May. 2014.

Rachel Dratch. Magmire. Feb. 2011. Online Photograph. Web. 14 May. 2014.

Beyonce.Croatia Week. Apr. 2013. Online Photograph. Web. 16 May. 2014.

Shania Twain. VIP photo. Online Photograph. Web. 17 May. 2014.

Brad Pitt. Us Weekly. 2014. Online Photograph. Web. 18 May. 2014.

Mind’s Eye Influences Visual Perception. Science Daily. 04 July. 2008. Web. 08 May. 2014.

Hom, Elaine J.What is the Golden Ratio?. Live science. 24 Jun. 2013. Web. 06 May. 2014.

In conclusion, there is only a slight correlation between the variance of one's facial measurement from the golden ratio to their desirability score. I hypothesized that the higher one's variance from the golden ratio was, the lower their desirability score was. According to by hypothesis, the correlation between the two variables should have been -1, but from my results the correlation between the variables is around -0.32, indicating that there is still a slight correlation as the correlation is still negative but the correlation is not strong.

There is only a slight correlation because there are a handful of celebrities that have high desirability scores and small variances but there were also celebrities like Brad Pitt and Shania Twain who had the smallest variance from the golden ratio but were the median in desirability score. There is also the outlier, which in this case is Drake, who has a slight effect on the correlation, as he is not seen to be near the slight trend that appears in the correlation graph. He is an outlier since he has the largest variance from the golden ratio but has a desirability score that is higher than two other celebrities who have a smaller variance from the golden ratio than him.
Divergence and Desirability Correlation
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