en>Someone not using his real name |
|
| Line 1: |
Line 1: |
| {{Odd polygon db|Odd polygon stat table|p15}}
| | She is recognized by the name of Myrtle Shryock. What I love performing is doing ceramics but I haven't produced a dime with it. California is exactly where her house is but she needs to transfer because of her family members. My day occupation is a meter reader.<br><br>Have a look at my page [http://Urlx.at/healthymealsdelivered68340 http://Urlx.at] |
| In [[geometry]], a '''pentadecagon''' (or '''pentakaidecagon''') is any 15-sided, 15-angled, [[polygon]].
| |
| | |
| ==Regular pentadecagon==
| |
| A [[Regular polygon|regular]] pentadecagon has interior angles of 156°, and with a side length ''a'', has an area given by
| |
| :<math>
| |
| \begin{align} 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 17.6424\,a^2.
| |
| \end{align}</math>
| |
| | |
| == Uses ==
| |
| [[File:3.10.15 vertex.png|160px]]<BR>A regular triangle, decagon, and pentadecagon can completely fill a plane vertex.
| |
| | |
| ===Construction===
| |
| A regular pentadecagon is [[constructible polygon|constructible]] using [[compass and straightedge]]:
| |
| | |
| [[File:Regular_Pentadecagon_Inscribed_in_a_Circle.gif]]<br>Construction of a regular pentadecagon
| |
| | |
| Construction of a regular pentadecagon is Proposition XVI of Book IV of [[Euclid's Elements|Euclid's ''Elements'']].<ref>William Dunham, ''Journey Through Genius: The Great Theorems of Mathematics'', Penguin, 1991, ISBN 014014739X, p. 65.</ref>
| |
| | |
| ===Pentadecagrams===
| |
| There are 3 regular [[star polygon]]s: {15/2}, {15/4}, {15/7}, constructed from the same 15 vertices of a regular pentadecagon, but connected by skipping every second, forth, or seventh vertex respectively.
| |
| | |
| There are also three regular [[star figure]]s: {15/3}, {15/5}, {15/6}, the first being a compound of 3 [[pentagon]]s, the second a compound of 5 [[equilateral triangle]]s, and the third is a compound of 3 [[pentagram]]s.
| |
| | |
| ===Petrie polygons===
| |
| The regular pentadecagon is the [[Petrie polygon]] for one higher dimensional polytope, projected in a skew [[orthogonal projection]]:
| |
| | |
| {| class=wikitable
| |
| |- align=center
| |
| |[[File:14-simplex_t0.svg|150px]]<br>[[14-simplex]] (14D)
| |
| |}
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| ==External links==
| |
| *{{MathWorld|title=Pentadecagon|urlname=Pentadecagon}}
| |
| | |
| {{Polygons}}
| |
| | |
| [[Category:Polygons]]
| |
She is recognized by the name of Myrtle Shryock. What I love performing is doing ceramics but I haven't produced a dime with it. California is exactly where her house is but she needs to transfer because of her family members. My day occupation is a meter reader.
Have a look at my page http://Urlx.at