Size and Shape of [Palm] Trees (2C)

 Questions:

1. From your graph, does the height of the tree show a correlation with the diameter of the stem? Is the relationship linear or curvilinear? Interpret this result.
   • The height of the tree shows an overall linear correlation to the diameter of the trunk; however, there are a few trees that fall quite far from the line of best fit. We measured multiple species of palm trees, but did not note which species each tree was. We do know that most of the trees were of one species, so the outliers were likely trees of a different species. The majority of our trees were likely Bismarck Palms.
2. In animals, the strength supporting bone is related to the cross-sectional area of the bone. This results in different proportions for legs of heavy animals as seen in Figure 2.6. Do you see a similar trend in larger trees, which bear a proportionately heavier weight?
   • I do see a similar trend for most trees, although not all of them. This may be because we measured different types of palm trees.
3. If the strength of a tree trunk is proportional to its cross-sectional area, and weight of a tree is related to its volume, then what powers of your measurement variables (diameter and height) would be expected to yield a straight line on the above graph?
   • Half of the diameter (the radius) squared, multiplied by the height, would give you the volume of the tree trunk. The cross-sectional area can be calculated by squaring the radius and multiplying it by pi (3.14).
4. Using the tangent to measure the height of a tree is a classic application of trigonometry in a field study. Find a definition of the tangent. Why was this function used rather than a sine or cosine in our procedure? 

   • The tangent is defined as the “ratio of the opposite to the adjacent side of a right-angled triangle” (wordnetweb.princeton.edu/perl/webwn). This function was used opposed to sine or cosine because both of those functions require knowing the height of the tree in order to make the calculation, and if we knew the height, we wouldn't need to do a calculation at all.

   5. On your campus, what factors other than age of a tree could affect its height and diameter? Might one of these variables be affected more significantly than the other? How might these secondary factors affect your results?
   

   • Past extreme weather, proximity to other trees (especially non-palms), proximity to concrete, and species of the tree may have affected the height and diameter of the trees. It is likely that extreme weather had the most impact on my data set because most of the trees were quite close to concrete walkways, and some of the trees were curved near the top, likely as a result of high winds when the tree was young. While proximity to other trees likely had an impact, it doesn't seem significant as most of the trees were quite close to other trees, whether palm or not. These secondary factors could skew my results to numbers that are lower than expected from the species.
   
** Aidan Bailey and I worked together on this lab.