# apothem

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## ap·o·them

, apotheme (ap'ō-them, ap'ō-thēm),
A precipitate caused by long boiling of a vegetable infusion or by its exposure to air.
[G. apo, from, + thema, something set down, fr. tithēmi, to place]

## apothem

A line drawn from the edge of a polygon to its geometric centre, or vice versa.
References in periodicals archive ?
The area (A) of particle chambers was calculated from the mean edge length (l) using the equation for a regular hexagon in which A = (6al)/2, where a is the apothem. Particle volume (V) was estimated using the equation, V = [pi] * [r.sup.2]h - 4/3[pi] * [r.sup.3], where r is the radius of the particle and h is particle length.
If we let [P.sub.n] represent a regular polygon of n sides inscribed in a circle of radius r, and [P.sub.n] represent its perimeter and [a.sub.n] the length of its apothem. (An apothem is a perpendicular segment from the centre of a regular polygon to one of its sides.) Then it is clear that as the number n of sides of the polygon increases, the apothems get closer and closer to the radius of the circle and the perimeters of the polygons get close to the circumference of the circle.
Ganguli; "The Apotheosis of the Apothem," by Steven Schwartzman; "Relaxation Functions," by Homer B.
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