Pentadecagon

From Wikipedia, the free encyclopedia

A regular pentadecagon.
A regular pentadecagon.

In geometry, a pentadecagon is any 15-sided, 15-angled, polygon. A regular pentadecagon has interior angles of 156°, and with a side length a, has an area given by

A=\frac{15}{4}a^2 \cot \frac{\pi}{15} = \frac{15a^2}{8} \left( \sqrt{3}+\sqrt{15}+\sqrt{2}\sqrt{5+\sqrt{5}} \right) \simeq 17.6424a^2.


A regular pentadecagon is constructible with compass and straightedge. The following animation illustrates this process in 36 steps, and is adapted from a method given in Euclid's Elements, Book IV, Proposition 16. Note that the compass radius remains unaltered during steps 14 through 21.

Pentadecagon Construction Animation


Polygons
Triangle • Quadrilateral • Pentagon •Hexagon • Heptagon • Octagon • Enneagon (Nonagon) • Decagon • Hendecagon • Dodecagon • Triskaidecagon • Pentadecagon • Hexadecagon • Heptadecagon • Enneadecagon • Icosagon • Chiliagon • Myriagon
Retrieved from "http://en.wikipedia.org../../../p/e/n/Pentadecagon.html"
Advanced Search
Included Web Search Engines


Safe Search

close

Top Matching Results

Occasionally Search.com will highlight specialized results that are based on the context of your query. Examples of specialized results include specific links to news, images, or video.

Top Matching Results may highlight information from other Search.com pages, content from the CNET Network of sites, or third party content. The listings are based purely on relevance. Search.com does not receive payment for listings in this section but our partners that provide this data may get paid for listing these products.

Sponsored Links

This section contains paid listings which have been purchased by companies that want to have their sites appear for specific search terms and related content. These listings are administered, sorted and maintained by a third party and are not endorsed by Search.com.

Search Results

Search.com sends your search query to several search engines at one time and integrates the results into one list which has been sorted by relevance using Search.com's proprietary algorithm. You can customize the list of search engines included in your metasearch from the preferences.

The search engines that are used in your metasearch may allow companies to pay to have their Web sites included within the results. To view the Paid Inclusion policy for a specific search engine, please visit their Web site. Search.com does not accept payment or share revenue with any search engine partner for listings in this section.