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ERIC Number: EJ856231
Record Type: Journal
Publication Date: 2008-May
Pages: 9
Abstractor: As Provided
Reference Count: 0
ISBN: N/A
ISSN: ISSN-0746-8342
Squaring a Circular Segment
Gordon, Russell
College Mathematics Journal, v39 n3 p212-220 May 2008
Consider a circular segment (the smaller portion of a circle cut off by one of its chords) with chord length c and height h (the greatest distance from a point on the arc of the circle to the chord). Is there a simple formula involving c and h that can be used to closely approximate the area of this circular segment? Ancient Chinese and Egyptian records indicate the use of a formula based on a trapezoid to approximate this area, namely h(c+h)/2. Several centuries later, Archimedes discovered a formula (based on a triangle) that gives the exact area of a parabolic segment. Since a parabola can be used to approximate a circular arc, Archimedes' result yields 2ch/3 as another formula to approximate the area of the circular segment. A search for a better estimate, one that continues to rely on a quadratic function of c and h, reveals a much better approximation for this area than either of the ones mentioned thus far and generates some interesting elementary mathematics.
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