Nonagon

Template:Odd polygon db In geometry, a nonagon (or enneagon) is a nine-sided polygon.

The name "nonagon" is a prefix hybrid formation, from Latin (nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century. The name "enneagon" comes from Greek enneagonon (εννεα, nine + γωνον (from γωνία = corner)), and is arguably more correct, though somewhat less common.

A regular nonagon has internal angles of 140°. The area of a regular nonagon of side length a is given by

$A={\frac {9}{4}}a^{2}\cot {\frac {\pi }{9}}\simeq 6.18182\,a^{2}.$

Although a regular nonagon is not constructible with compass and straightedge there are methods of construction that produce very close approximations.

Graphs

The K₉ complete graph is often drawn as a regular nonagon with all 36 edges connected. This graph also represents an orthographic projection of the 9 vertices and 36 edges of the 8-simplex.

Pop culture references

They Might Be Giants have a song entitled "Nonagon" on their children's album "Here Come the 123s." It refers to both an attendee at a party at which "everybody in the party is a many-sided polygon" and a dance they perform at this party.[1]

References

• Weisstein, Eric W. "Nonagon". MathWorld.

See also

• Enneagram (nonagram)

External links

• Properties of a Nonagon (with interactive animation)
• Nonagrams