Illinois Junior Academy of Science - Yearbook (Urbana, IL)

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To learn about the symmetric curves I applied both synthetic and analytic geometry. Synthetic or Enchidean geometry involves postulates - basic statements that are accepted without proof - and theorems - logically reasoned statements based from previously accepted or proved postu- lates or theorems. This geometry's fundamental tools are points, lines and planes. Analytic geometry primarily uses algebra. Applying both I am now able to reason the answers to a practical problem involving conics. For my demonstration and booklet I drew diagrams showing how conics can be formed by a straight cut in a cone as well as diagrams of conics drawn from an algebraic expression on a coordinate plane. By using cones that I molded from rock hard water putty and then cut and sanded, I proved three-dimensionally that a conic is a plane section of a cone. Because of their properties conics can only be drawn by special apparatuses, one of which I partly developed and built. This was the only working part of my research project.

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PHYSICS