Measuring Your World
Summary
The Measuring Your World project is a project that focuses on the recording of physical attributes (in this case, length, height, and width) and using that to calculate for other item attributes, like area and volume. In doing this, we learned new concepts, types of math, and formulas to help us solve such problems faster. We started out with the more conceptual side of calculating values, starting with trigonometry, and moving on to calculating the volume of more complicated shapes with limited information.
Concepts Learned
TrigonometryBefore this project, trigonometry was completely new to me, and as you could expect at the time, very confusing. Trigonometry is the math used to convert angles in a right triangle to side length ratios, rotating around one angle chosen, called theta, denoted with the respective greek symbol; Ø
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Pythagorean TheorumPythagorean theorem (http://i.imgur.com/GqMjBWI.gif) is a way of calculating the side length of any triangle, provided the knowledge of the other two sides' length.
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Qualities of 2D ShapesIn class, we learned a helpful formula that, given the side count, calculated for the total interior angle amount. For instance, a triangle has 3 sides and 180˚ of interior angle, calculated by: (((Side Count)-2)*180)
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Volume of Simple ShapesWhen we moved to calculating the volume of shapes, we started with simple shapes that possessed an unchanging Height, Length, and Width, and calculated their volume with the simple formula of (L*W*H)
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Volume of Complex Shapes |
Volume Formulas |
We later moved on to more complex shapes such as Frustums, Cones, and pyramids that had changing, yet linear dimensions. We learned to calculate these in a way not dissimilar to regular shapes, but with some extra values added to the mix, thanks to the property of yangmas; right pyramids created from a third of a cube's volume.
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For more complex shapes, such as Spheres, we learned an array of new formulas that allow us to calculate volume with simple values such as the radius or circumference.
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Final Product: Volume of Object of Choice (Presentation Below)
Final Product Reflection
Personally, I enjoyed calculating the area of this ship, especially when equipped with the knowledge required to do so thoroughly and correctly (to a 4 decimal point accuracy). Personally, I'm glad that I took on the simpler TOS Enterprise rather than a later vessel, because the hull is much more geometric and basic. Any more complexity, and the calculations would be far askew. I am disappointed that I could not find the volume of some specific parts of the ship, mainly due to the fact that some values needed were incalculable (at least by my knowledge). One specific part that comes to mind would be the neck calculation. The neck of the enterprise sat perpendicular on a frustum cone that made up the engineering section. Had this been a regular cylinder or a simpler frustum, I might've been able to calculate the correct volume for such a shape, however Dr. Drew advised that I would need to use a calculus function in order to accurately determine the lost space in the neck shape. And of course, it was fun to go up and give a presentation on this, because I love Star Trek and the fact that I can use it in Math as a legitimate project piece.
Measure Your World Reflection
Like the calculation of the Enterprise Volume, I enjoyed this project, primarily because it contained valuable information for me. These things that I learned allowed me to do things I couldn't possibly hope to calculate before. This applies especially to what we learned as far as trigonometry; converting angles into side length ratios and vice-versa. This also applies to the qualities of special triangles, such as side ratios in 30/60/90 and 45/45/90 triangles. These, are actually things I have wanted to know, things I needed to know, that will help me in the future. Now, by this, I don't want to imply past math was not helpful, but this is simply something that everyone needs to know; a necessary math. In creating the final product (Enterprise Volume), the most important Habit of a Mathematician I used was 'Taking Apart And Putting Back Together'. As you can see in my lengthy presentation, this was a tactic employed generously, with the whole ship being taken down to the domes on the nacelles (Bussard Collectors). Another useful Habit was the act of being Systematic. Finding the volumes of said parts of the ship was something that needs to done in some mindset of order and caution. When you are dealing with an upward of 20 separate parts of the damn thing, you need to avoid any misunderstandings (although my calculation papers were anything but orderly to the average person). In addition to these Habits, I frequently used the magical math of trigonometry to find the much needed angles required to calculate frustums, cones, and oblique rectangular prisms.