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ERIC Number: EJ856231
Record Type: Journal
Publication Date: 2008-May
Pages: 9
Abstractor: As Provided
Reference Count: 0
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.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A