IB Mathematics Internal Assessment
This project was an assignment I undertook over the last year of highschool, as part of the requirements for my Mathematics Class. This project was supposed to be a relatively rigorous and concise research paper into a topic of my choosing, after discussion with my teacher. Through this project, I got my first introduction to structured research, and writing a report, especially in mathematics, and the sciences. Guided and structured research is an extremely important skill to have in the sciences, especially for someone looking to enter a research position.
The topic chosen by me was an investigation of the Archimedes Principle, which relates the surface area of an object to its buoyancy, and ultimately its carrying capacity, without sinking underwater. I then used this principle to investigate various mathematical equations, in order to produce the optimal shape for a boat, that maximised carrying capacity. I began by identifying certain shapes that seemed, based on prior understanding, to have relatively large carrying capacity. I also took a hollow cube as a control case, in order to compare the relative gains with change in shape. While in retrospect this approach was rather naive, since each shape is rather simple, and are produced by integrating simple curves, it serves as a display of a solid understanding of the scientific approach, even before entering college.
Looking at the choices for each curve, displays the idea of iteration, and controlling for variables. Each boat has with it a simple explanation of what kind of boat it will yield, describing its length, breadth, and depth. This allows for a good comparison about how a change in each dimension will affect the capacity of the boat. Further, this project also displays my understanding of ensuring a fair comparison, since each boat was constructed to be of roughly similar size, fitting within an 8x8x8 cube. This size constraint allowed for me to disregard scale, since scaling up a boat would yield a higher carrying capacity, but not having consistent size would yield an unfair comparison.
The topic chosen by me was an investigation of the Archimedes Principle, which relates the surface area of an object to its buoyancy, and ultimately its carrying capacity, without sinking underwater. I then used this principle to investigate various mathematical equations, in order to produce the optimal shape for a boat, that maximised carrying capacity. I began by identifying certain shapes that seemed, based on prior understanding, to have relatively large carrying capacity. I also took a hollow cube as a control case, in order to compare the relative gains with change in shape. While in retrospect this approach was rather naive, since each shape is rather simple, and are produced by integrating simple curves, it serves as a display of a solid understanding of the scientific approach, even before entering college.
Looking at the choices for each curve, displays the idea of iteration, and controlling for variables. Each boat has with it a simple explanation of what kind of boat it will yield, describing its length, breadth, and depth. This allows for a good comparison about how a change in each dimension will affect the capacity of the boat. Further, this project also displays my understanding of ensuring a fair comparison, since each boat was constructed to be of roughly similar size, fitting within an 8x8x8 cube. This size constraint allowed for me to disregard scale, since scaling up a boat would yield a higher carrying capacity, but not having consistent size would yield an unfair comparison.
Physics
at
University of Maryland, College Park
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