JSU Student Symposium 2020
 
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Title

Expanding "the Quadrature of a Parabola" to Cubic Functions

Date

2-13-2020

Faculty Mentor

Jaedeok Kim, Mathematical, Computing & Information Sciences

Files

Submission Type

Paper

Location

Houston Cole Library, 11th Floor | 1:30-1:40 p.m.

Description

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.

Keywords

student presentations, student papers, formulas, algebra, calculus

Rights

This video is the property of Jacksonville State University and is intended for non-commercial use. Video and images may be copied for personal use, research, teaching or any "fair use" as defined by copyright law. Users are asked to acknowledge Jacksonville State University. For more information, please contact digitalcommons@jsu.edu.

Disciplines

Algebraic Geometry

Presentation Information

Junkins, B. (2020, 13 February). Expanding "the quadrature of a parabola" to cubic runctions. Paper presented at the 2020 JSU Student Symposium, Jacksonville State University, Jacksonville, AL.

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