**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.

Descriptors: Geometric Concepts, Geometry, College Mathematics, Mathematics Instruction, Problem Solving, Mathematical Formulas

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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