IB Internal Assessment Investigation of arm span-height ratio in relation to proportionality of measurements Introduction This study was designed in order to determine the accuracy of the proportion of man as outlined in The Vitruvian Man (1940) by Leonardo da Vinci. Da Vinci’s renowned drawing was based on the Roman architect Vitruvius’ description of man. Vitruvius stated that, “For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height. The ratio in question is the arm span to height ratio, specifically for Asian-descent males.
The accepted unit of measurement for this study is the centimeter (SI system of units). Should the proportions of arm span to height in Asian-descent males prove to be different than those outlined by Vitruvius, the ‘perfect man’ ideal will be nullified. The consistencies when measuring the selected Asian-descent males were: 1. The environment- All subjects were tested in the same school. 2. Age- All subjects were between the 16-18 year ranges.
. Conditions- All subjects were made to stand barefoot when measuring height, and when measuring arm span, the length between the tip of the middle finger on the left hand to the tip of the middle finger on the right hand were considered. Nails were not measured or counted, nor was hair. 4.
Device- All subjects were measured using a 25’ (or 762 cm) long tape measure, made by Stanley Co. Systematic error was considered, with a range of ±0. 5 cm. Once the systematic error is taken into consideration, the proportions measured are more accurate.
In order to validate the findings and give depth to them, ten subjects were measured, and their results analyzed. Hypothesis The proportions found in Asian-descent males differ from those stated in The Vitruvian Man. This theory is due to multiple factors. Firstly, da Vinci and Vitruvius, being of European origin, were only able to measure European-descent men. If their proposal does not hold true for all races and genders, then it can be deemed invalid.
Although the gender remains constant, the geographical and cultural origin of the subject has changed, which becomes another factor.Furthermore, the technology being used by modern scientists with that of da Vinci’s time are erratically contrasting, hence the error of measurement could have been greater for him. Materials * 10 Asian-descent male subjects * Pencil * Paper * Measuring tape/ meter stick * Calculator/Laptop Method 1. Ask each subject to remove shoes and socks and stand straight.
2. Using a measuring tape or meter stick, measure from the base of the foot to the highest part of the body, excluding hair. 3. Note down the height. 4. Ask the subject to extend their arms horizontally as widely as possible.
. Measure from the tip of the left middle finger to the tip of the right middle finger, excluding nails. 6. Note down the arm span. 7. Repeat for all subjects until ten heights and ten arm spans are measured.
Results Subject| Height(cm)| Arm span(cm)| 1| 177. 8| 177. 5| 2| 176. 53| 176. 5| 3| 172.
72| 172. 6| 4| 175. 26| 175| 5| 152. 4| 152.
5| 6| 161. 29| 161. 3| 7| 162. 56| 162. 5| 8| 168.
91| 169. 1| 9| 165. 1| 165| 10| 173. 35| 173. 2| 11| 156.
21| 156| The values, as stated above, are in centimeters. As seen in the table, the values of height range from 152. to 177. 8 cm.
The values of arm span range from 152. 5 to 177. 5 cm. When systematic error is taken into account, ±0. 5 cm, the proportions are almost identical to The Vitruvian Man’s proportions. From these data points, other statistics were determined as well.
All data are accurate to + or – 0. 05 cm. Variables Independent Variable: Ethnicity/Gender (in this case Asian-descent male) Dependent Variable: Proportions Measured Constants/Controlled Variables: age, environment, conditions, measuring device ConclusionThe data proves that da Vinci and Vitruvius’ proportions are legitimate, and that they hold true for all races, at the very least, for Asians as well as Europeans. Because the uncertainties of both the mean and standard deviation do not overlap, this is conclusive evidence that the data is significant.
While all subjects tested were of Asian descent, there is a gray area between Oriental Asians (Chinese, Koreans, Taiwanese, Vietnamese, etc. ) and Indians. While the Indian subcontinent is technically part of Asia, the cultures are completely different, as are the environmental factors.Ultimately, the null hypothesis was proved: that there was no difference between The Vitruvian Man‘s proportions and Asian-descent men’s proportions.
In the future, more trials might ensure an even higher level of accuracy. Also, if the subjects measured are all from the same part of Asia, wherever it may be, that might eliminate environmental factors as a variable. Works Cited “Ten Books on Architecture by Vitruvius”, 10/15/11, Web, 10/19/11, http://www. gutenberg.
org/files/20239/20239-h/29239-h. htm#Page_72
