Application: Finding the Length of a Christmas Light on a Tree (Essay Sample)

Application of Geometry: Finding the Length of a Christmas Light on a Tree
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Application of Geometry: Finding the Length of a Christmas Light on a Tree
Christmas tree is a fir tree that is dressed with light every Christmas. The tree grows and it is pruned (Uszak, 2016). The tree takes the shape of a cone and with lights on, it appears attractive and beautiful. The bulbs are on a single string that winds from the top to the bottom of the tree (Uszak, 2016). For instance, most of the Christmas trees have one hundred bulbs that are spaced three hundred millimeters apart. For a Christmas tree of height, h, (cm), the following formulas are used to determine the number of decorations that should appear on the tree (Uszak, 2016). To find the number of baubles to put on the tree, the artist uses the formula h √17 / 20. An individual can determine the length of lights in centimeters using the formula π h, also, one can use the formula 13 π h / 8 to find the length of the tinsel in centimeters (Uszak, 2016). In addition, an artist can employ the formula h / 10 to find the height of the star in centimeters. Noticeably, all the formulas listed above are linear to h.
Normally, while applying the formulas above, one assumes that the baubles are spread homogeneously over conical the tree surface, with σ as its surface density and radius of r. A person can apply the formula σ π r √ (r²+h²) to find the number of baubles (Uszak, 2016). Since the artists do not decorate the bottom surface of the tree, they apply the formula of an open cone to find the number of baubles that the tree needs. In any case, there is a unique relationship between r and h, the artist would only measure the height of the tree. For most Christmas tree, the opening angle α of such arts is within the range of 21 ± 4°, and therefore, for most trees, the formula r = h tan (21 ± 4°) = h (0.38 ± 0.08), is applied (Uszak, 2016). The improved formula-in-h to calculate the number of bubbles, σ π 0.38 h √ (0.382+12) h = 0.41 σ π h², is applied (Uszak, 2016). The figure 1 below was obtained from sites.google.com/site/calculatinghistory/home/christmas-tree-formulas (Smeets, 2013). The below diagram is the one that has been used to obtain the above formulas.