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Difference between revisions of "Apothem"

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''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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012780/a0127801.png" />-gon is equal to the radius of the circle inscribed in it and is connected with the side of the polygon, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012780/a0127802.png" />, and with its surface area <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012780/a0127803.png" /> by the relations:
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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:
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012780/a0127804.png" /></td> </tr></table>
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$$a_n=2r_n\tan\frac\pi n,\quad S_n=nr_n^2\tan\frac\pi n.$$
  
 
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