apothem

(redirected from apothems)
Also found in: Medical, Encyclopedia.

ap·o·them

 (ăp′ə-thĕm′)
n.
The perpendicular distance from the center of a regular polygon to any of its sides.
[apo- + Greek thema, something laid down; see theme.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

apothem

(ˈæpəˌθɛm)
n
(Mathematics) the perpendicular line or distance from the centre of a regular polygon to any of its sides
[C20: from apo- + Greek thema, from tithenai to place]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

ap•o•them

(ˈæp əˌθɛm)

n.
a perpendicular from the center of a regular polygon to one of its sides.
[1855–60; < French apothème]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
Mentioned in ?
References in periodicals archive ?
-- Normal coordinates of the straight lines containing the sides: {([p.sub.1], [[theta].sub.1]), ([p.sub.2], [[theta].sub.2]), ..., ([p.sub.n], [[theta].sub.n])}- The 'apothems' {[p.sub.i]} are all positive if O[member of][K.sup.*], but not otherwise.
Uniqueness properties of the invariator, leading to simple computations
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.
Now [P.sub.1n] and [P.sub.2n] are similar, so the ratio of their perimeters is in the same ratio as the lengths of their corresponding sides, which in turn are in the same ratios as the lengths of their apothems, [a.sub.1] and [a.sub.2]; that is
An ordinary but surprisingly powerful theorem

Dictionary browser ?
Full browser ?