Expanding "the Quadrature of a Parabola" to Cubic Functions
Jaedeok Kim, Mathematical, Computing & Information Sciences
Houston Cole Library, 11th Floor | 1:30-1:40 p.m.
A brief summary of Archimedes' "Quadrature of the Parabola" is given showing the use of recursively defined triangles to find the area bounded by a parabola and a line. A special relationship between the initial inscribed triangle and the total bounded area was shown in his work, and this idea of finding a relationship between the initial triangle and bounded area is then expanded to a general depressed cubic function. The derivation of Vieta's formulas is shown, and the formulas are used to greatly simplify the algebra and calculus of this expansion. After finding the relationship, a pattern from the quadratic to cubic case is found, and it is conjectured that this pattern holds for any degree polynomials of a certain depressed form.
student presentations, student papers, formulas, algebra, calculus
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Junkins, Benjamin, "Expanding "the Quadrature of a Parabola" to Cubic Functions" (2020). JSU Student Symposium 2020. 22.