ERIC Number: EJ938162
Record Type: Journal
Publication Date: 2006-Jan
Abstractor: As Provided
Reference Count: 0
Archimedes Quadrature of the Parabola: A Mechanical View
Oster, Thomas J.
College Mathematics Journal, v37 n1 p24-28 Jan 2006
In his famous quadrature of the parabola, Archimedes found the area of the region bounded by a parabola and a chord. His method was to fill the region with infinitely many triangles each of whose area he could calculate. In his solution, he stated, without proof, three preliminary propositions about parabolas that were known in his time, but are not widely known today. It is the purpose of this short paper to prove the ideas presented in these obscure propositions so that a complete presentation of Archimedes' solution can be given. Our proofs are novel in that they are "mechanical"; that is, they use simple ideas from elementary physics rather than geometry. We use the fact that a particle, not acted on by friction, in motion near the surface of the earth, has a parabolic trajectory. The proofs given this way are very simple.
Descriptors: Mathematics Instruction, College Mathematics, Geometric Concepts, Validity, Mathematical Logic, Physics, Geometry, Motion
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Authoring Institution: N/A