**ERIC Number:**EJ938162

**Record Type:**Journal

**Publication Date:**2006-Jan

**Pages:**5

**Abstractor:**As Provided

**Reference Count:**0

**ISBN:**N/A

**ISSN:**ISSN-0746-8342

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

Mathematical Association of America. 1529 Eighteenth Street NW, Washington, DC 20036. Tel: 800-741-9415; Tel: 202-387-5200; Fax: 202-387-1208; e-mail: maahq@maa.org; Web site: http://www.maa.org/pubs/cmj.html

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A