The Physics Factbook™
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The purpose of this experiment is to verify the proportionality of the human body.
Nature has always been admired for its patterns and symmetry. The human body is an example of nature's proportion. Phi, the Golden Number 1.618, is a proportion found in many areas of the natural world as well as in the structure of the human body. Many of the bones that form our skeleton are thought to have a proportional relationship of 1:1.618. The human body itself is believed to be symmetrical as displayed in Leonardo DaVinci's Vitruvian Man in which a man with outstretched arms fits exactly into a square.
The data collected can be found here in excel format.
|Wingspan (cm)||Height (cm)||Wingspan-Height proportion||Forearm+Hand (cm)||Forearm (cm)||ForearmHand-Forearm proportion|
It was previously believed that the wingspan of a person is equal to the height of that same person. It is also believed that the proportion of a person's forearm to their hand is in a ratio of 1.6.
The proportion of wingspan to height is found by dividing the wingspan of the person over their measured height. Graphically the proportion of height to wingspan is represented by coefficient A on the proportional fit equation, y=A*x, shown on the Wingspan vs Height graph. The proportion was found to be 1.023.
To find the proportion of forearm+hand to forearm, we divided the forearm+hand of the person over their measured forearm. Graphically the proportion of forearm+hand to forearm is represented by coefficient A on the proportional fit equation, y=A*x, shown on the forearm+hand vs forearm graph. The proportion was found to be 1.715
To further statistically analyze the calculated measurements, we performed a t-test to determine whether the proportions found were significantly different to the established values.
|Conditions for using a t-test
|HO: Body Proportion Height/Wingspan = 1
HA: Body Proportion Height/Wingspan 1
|HO: Body Proportion Forearm Hand/Forearm = 1.618
HA: Body Proportion Forearm Hand/Forearm ≠ 1.618
|n = 24 people
y = 1.044
s = 0.1166
t = 1.835
|n = 25 people
y = 1.698
s = 0.0449
t = 10.797
|p = 0.079||p = 1.076E-10|
|The p-value of 0.079 is not small enough for us to reject the hypothesis that the true mean body proportion is 1. We conclude that there is not enough evidence to say the proportion is not 1.||The p-value of 1.076E-10 is small enough for us to reject the hypothesis that the true mean body proportion is 1.618. We conclude that there is enough evidence to say the proportion is not 1.618|
We found the proportion of Height to Wingspan to be 1.023 which is within 2.3% error of the established value of 1. The one-sample T-test concluded that there is not enough evidence to say the proportion is not 1.
We found the proportion of Forearm+Hand to forearm to be 1.715 which is within 6% error of the established value of 1.618. The one-sample T-test concluded that there is enough evidence to say the proportion is not 1.618, phi.
Stacey Johnson, Kristine McPherson -- 2006
Students Choice pages in The Physics Factbook™ for 2006
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