Difference between revisions of "Apothem"
From Encyclopedia of Mathematics
(Importing text file) |
(TeX) |
||
| Line 1: | Line 1: | ||
| + | {{TEX|done}} | ||
''of a regular polygon'' | ''of a regular polygon'' | ||
| − | The segment (and its length) of a perpendicular dropped from the centre of the regular polygon onto any of its sides. The apothem of a regular | + | The segment (and its length) of a perpendicular dropped from the centre of the regular polygon onto any of its sides. The apothem of a regular $n$-gon is equal to the radius of the circle inscribed in it and is connected with the side of the polygon, $a_n$, and with its surface area $S_n$ by the relations: |
| − | + | $$a_n=2r_n\tan\frac\pi n,\quad S_n=nr_n^2\tan\frac\pi n.$$ | |
The apothem of a regular pyramid is the height of its (side) face. | The apothem of a regular pyramid is the height of its (side) face. | ||
Latest revision as of 15:30, 13 October 2014
of a regular polygon
The segment (and its length) of a perpendicular dropped from the centre of the regular polygon onto any of its sides. The apothem of a regular $n$-gon is equal to the radius of the circle inscribed in it and is connected with the side of the polygon, $a_n$, and with its surface area $S_n$ by the relations:
$$a_n=2r_n\tan\frac\pi n,\quad S_n=nr_n^2\tan\frac\pi n.$$
The apothem of a regular pyramid is the height of its (side) face.
How to Cite This Entry:
Apothem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Apothem&oldid=17522
Apothem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Apothem&oldid=17522