Research Question:

Do we have the ideal proportion?

The length of the outspread arms is equal to the height of a man The distance from the elbow to the tip of the hand is a quarter of the height of the man The maximum width of the shoulders is a quarter of the height of a man Data Collection:

Raw Data:

Table #1: Measure of the Outspread Arm, Height, from Elbow to the Tip of the Fingers, and Width of Shoulders (cm) (per person)

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Name

Outspread arm /cm +/-1

Height /cm +/- 1

From the elbow to the tip of the fingers /cm +/- 1

Width of shoulders /cm +/-1

Silvana Chumaceiro

170

163

43

43

Anna Marrone

165

163

41

42

Sabrina Casilla

158

156

37

54

Alberto Gonzalez

180

174

48

65

Yanuara Ramirez

164

164

41

42

Maria Semidey

156

156

39

41

Camille Quintero

159

160

43

39

Deborah Vasquez

157

162

39

43

Maria Pappagallo

175

165

43

47

Amanda Kauffman

166

166

39

43

Luis Ramirez

180

170

43

47

Processed Data:

Table #2: ¼ Measurement of Height (cm) (per person)

Name

1/4 Height /cm +/-1.00

Silvana Chumaceiro

40.75

Anna Marrone

40.75

Sabrina Casilla

39.00

Alberto Gonzalez

43.50

Yanuara Ramirez

41.00

Maria Semidey

39.00

Camille Quintero

40.00

Deborah Vasquez

40.50

Maria Pappagallo

41.25

Amanda Kauffman

40.50

Luis Ramirez

42.25

Table #3: Mean and Standard Deviation of the Outspread Arm, Height, From the Elbow to the Tip of the Fingers, Width of Shoulders, and ¼ Height + the T-Test of the Height & Outspread Arm; From Elbow to Tip of Fingers & ¼ Height; Shoulders & ¼ Height

Outspread arm /cm +/-11

Height /cm +/- 11

From the elbow to the tip of the fingers /cm +/- 11

Width of shoulders /cm +/- 11

1/4 Height /cm +/- 11

Mean

166.364

163.545

41.909

45.727

40.886

Standard Deviation

8.869

5.373

3.048

7.578

1.343

Table #4: The T-Test and P-Value of the Height & Outspread Arm, From Elbow to Tip of Fingers & ¼ Height, and Shoulders & ¼ Height T-Test

Height & Outspread Arm

From Elbow to Tip of Fingers & 1/4 Height

Shoulders & 1/4 Height

P-Value

0.378

0. 321

0. 050

Calculations:

(These calculations are based on excel formulas)

¼ of Height:

Height / 4

Mean:

=AVERAGE(Data)

Standard Deviation:

=STDEV(Data)

T-Test:

=TTEST(Data, Data2,2,2)

Graphs:

Graph #1: Correlation of the height and the outspread arm of every tester(cm)

Graph #2: Correlation from the elbow to the tip of the toes and quarter height of every tester

Graph #3: Correlation of the width of the shoulders and quarter height of every tester Graph #3.1: Correlation of measurements or uncorrelated points in the graph

Graph #3.2:

Graph #4: The mean of the height and the outspread arm with their error bars (standard deviation) (cm)

Graph #5: The mean of the forearm and ¼ height with their error bars (standard deviation)(cm)

Graph #6: The mean of the width of shoulders and ¼ height with their error bars (standard deviation) (cm)

Conclusion:

Around 20 or 30 years B.C, a Roman architect called Marcus Vitruvius came up with the idea of the perfect man. Since he was an arquitect, he also applied this theory to buildings, stating which were the perfect proportions for a human and for a building. Later on, around the year 1490, the artist and painter Leonardo Da Vinci decided to keep examining about his statement. His famous drawing consists on a man with straight arms and legs, inside a square that is inside a circle, the exactly same idea of Vitruvius. “He showed that the ‘ideal’ human body fitted precisely into both a circle and a square, and he thus illustrated the link that he believed existed between perfect geometric forms and the perfect body”(The British Library Board). According with Natalie Wolchover the circle is shown as a divine symbol and the square as the earthly symbol. This idea relates to the ancient belief that the man was a tiny expression of the entire universe, which is now called ‘microcosm’.

As a class, we were asked to test the validity of the Da Vinci’s Vitruvian man. We recorded the information of everyone from the class, measuring the length of the outspread arms, the height, the distance from the elbow to the tip of the hand and the maximum width of the shoulders. Our goal was to discover if our dimensions settled with the ideal humans proportion according to Da Vinci’s Vitruvian man. Da Vinci explained that for a human to have perfect proportions need to follow the next criterias: the length of the outspread arms needs to be equal to the height of the man, the distance from the elbow to the tip of the hand needs to be ¼ of the height of man, and the maximum width of the shoulders needs to be ¼ of the height of the man.

After going through this whole process I got into a very concise conclusion, just two people in my class have the ideal human proportions. Yanuara Ramirez and Maria Semidey are the only ones who fit into the three of the statements made by Da Vinci and Vitruvius.

As is shown on table #1 and table #2, Yanuara Ramirez’s length of the outspread arms is equal to her height; her distance from the elbow to the tip of her hand equals a ¼ of her height, same situation occurs on Maria Semidey’s measurements. But on the third criteria you can see there is a difference between the maximum of their shoulders and their heights a difference of 1 cm. Even though their measurements have a difference of one cm, we can still say their proportions are idea, since we are account the uncertainties of +/- 1.

Several of my other classmates followed several criteria but at the end they didn’t fit exactly, for example as it’s shown on table #1 and table #2, Amanda Kauffman’s length of the outspread arms is equal to her height, and her distance from the elbow to the tip of her hand is a ¼ of her height as well, but when it comes to the third criteria, the maximum width of the shoulders isn’t a 1/4 of her height. The difference is about to 4 cm, which is an extremely small difference, since the maximum of her shoulders is about 39 cm and the ¼ of her height is about 43 cm.

Evaluation:

Due to the fact that the Da Vinci’s Vitruvian man lab demonstrated failure on the past examinations, we can feel free to assume that many errors are shown in this experiment.

The first error noticed is the fact that we measured everything with a small measuring tape instead of a big measuring tape, which didn’t help since we were taller and bigger than the measuring tape, so we had to use two measuring tapes added together. Using a small measuring tape to find out these measurements ended being extremely inaccurate. After data collection we were not really sure if the numbers we got were real, and it probably affected a lot on the way the results came out. The lab activity validity started to be questionable now.

By the time we were looking for the four measurements needed just one group of people from the class was using a measuring tape, the rest of the class were using two small ones (so they could have the same length). The way it worked was to put one in the top of the other and then add the numbers, which was hard for the person who was measuring since he didn’t have enough hands to hold the small measuring tape in the bottom, in the middle (place in which both tapes were combined) and in the top. If one of the measuring tapes we were using (top or bottom) moved a little bit, then the whole addition will change and the final result will end being inaccurate.

A proposed solution to this error will be measure all of the quantities again with a big measuring tape, in this way, we could make sure that all of the measurements are more precise and that no movement of the person with

the tape was going to affect on the validity of the research.

Another error noticed is the fact that you can always make a mistake with the numbers and get confused, so maybe the numbers you got aren’t real. A great solution to this error will be measuring at least three times each of the four requirements, which at the end will give us a more specific, secure, and valid answer. If we make another two measurements and we still get different numbers, we need to keep re-making this process until we start getting the same answer over and over again after repetitive results.

Another big error was noticed on the width of the shoulders measurements specifically, since some people didn’t know from which to which point it was, so in that way some people got a very inaccurate difference between this number and the ¼ of the height of a man. A good example that is shown is on table #1 and table #2, were Sabrina Casilla and Alberto Gonzalez got a lot of difference between this two measurements. Sabrina’s width of the shoulders is equal to 54 cm as is shown in the first table, and the ¼ of the height of a mans equals to 39. In the other hand, Alberto’s measurements also had a huge difference between them. His width of the shoulders is equal to 65, and 1/4 of his height equals to 43.50. After inspecting those numbers we can conclude that there is an error, since the rest of the students show on table #1 and table #2 do not have a difference higher than three cm between the numbers as both of this students had. This numbers are very inaccurate since the width of the shoulders and the ¼ of the height are suppose to be exactly the same, and this is such a huge difference.

A solution to this problem could be measuring the width of the shoulders and the ¼ of height of this students again, if we still get such a huge difference between both numbers, then the solution could be measuring the four principles again for this two people, at least 3 or 4 times, until the numbers we get are much more accurate.

One limitation I observed was the fact that most of us, the students, are still in a transitory age, which means we are still going through the process of developing physically. Since we are not entirely developed we are

not a secure source to prove if this statement is true or false. Our legs are not entirely developed yet, either our arms or the rest of our body.

Another limitation I found was the fact that we tested the validity on man and women, which variance wasn’t explain on the theory. Men and women may not have the same proportions as just man. This affected the research because women composed most of the class, so there were only two men (Alberto and Luis).

The last limitation founded was the fact that this research was made hundreds and thousands years ago by Vitruvius and Da Vinci, but with evolution human sizes may have changes and the proportions may have also changed, this effect was also reflected in the lab results.

APA Citation:

The British Library Board. (n.d.). Retrieved from http://www.bl.uk/learning/artimages/bodies/vitruvius/proportion.html Natalie Wolchover (e.g. 2011). Did Leonardo da Vinci Copy his Famous ‘Vitruvian Man?’. Retrieved from http://www.livescience.com/18183-leonardo-da-vinci-copy-famous-vitruvian-man.html Vitruvian Man. (n.d.). Retrieved from http://www.bbc.co.uk/science/leonardo/gallery/vitruvian.shtml