Definition:Regular Polygon/Apothem

Definition

The apothem of a regular polygon $P$ is defined as the perpendicular distance from the center of $P$ to one of its sides.

In the above, the length of $OM$ is the apothem of the regular polygon.

Also known as

The apothem of a regular polygon is also known as its short radius.

Also see

• Regular Polygon can be Circumscribed around Circle

• Definition:Long Radius of Regular Polygon

• Results about apothems can be found here.

Linguistic Note

The word apothem is pronounced ap-o-th'm (the last syllable with as little stress as the second).

It comes from Ancient Greek ἀπόθεμα (apóthema), meaning deposit, from:

ἀπό (apó), meaning off or away

θέμα (théma), meaning that which is laid down.

Compare the similar but unrelated word apothegm or apophthegm.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): apothem
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polygon
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): apothem
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polygon
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): apothem
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): apothem