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{{Odd polygon db|Odd polygon stat table|p11}}
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In [[geometry]], a '''hendecagon''' (also '''undecagon'''<ref>[http://www.mathopenref.com/undecagon.html Undecagon Definition – Math Open Reference]</ref>) is an 11-sided [[polygon]]. (The name ''hendecagon'', from Greek ''hendeka'' "eleven" and ''gon–'' "corner", is often preferred to the hybrid ''undecagon'', whose first syllable ''un–'' is Latin for "one".<ref>[http://mathworld.wolfram.com/Hendecagon.html Hendecagon – from Wolfram MathWorld<!--Bot generated title-->]</ref>)
 
==Regular hendecagon==
A regular hendecagon has [[internal angle]]s of 147.<span style="text-decoration: overline">27</span> [[degree (angle)|degrees]].<ref>{{citation|title=Glencoe mathematics: applications and connections|first=Kay|last=McClain|publisher=Glencoe/McGraw-Hill|year=1998|isbn=9780028330549|page=357}}.</ref> The area of a regular hendecagon with side length ''a'' is given by<ref>{{citation|title=Elements of Plane and Spherical Trigonometry: With Their Applications to Mensuration, Surveying, and Navigation|first=Elias|last=Loomis|publisher=Harper|year=1886|page=72|url=http://books.google.com/books?id=eqELAAAAYAAJ&pg=PA72}}.</ref>
:<math>A = \frac{11}{4}a^2 \cot \frac{\pi}{11} \simeq 9.36564\,a^2.</math>
 
A regular hendecagon is not [[Constructible polygon|constructible]] with [[compass and straightedge]].<ref>As [[Carl Friedrich Gauss|Gauss]] proved, a polygon with a prime number ''p'' of sides can be constructed if and only if ''p''&nbsp;&minus;&nbsp;1 is a [[power of two]], not true for 11. See {{citation|title=Mathematical Thought From Ancient to Modern Times|volume=2|first=Morris|last=Kline|authorlink=Morris Kline|publisher=Oxford University Press|year=1990|isbn=9780199840427|pages=753–754|url=http://books.google.com/books?id=VOcUBvbUXlEC&pg=PA753}}.</ref> Because 11 is not a [[Pierpont prime]], construction of a regular hendecagon is still impossible [[neusis construction|even with the usage of an angle trisector]].
 
Close approximations to the regular hendecagon can be constructed, however. For instance, the ancient Greek mathematicians approximated the side length of a hendecagon inscribed in a [[unit circle]] as being 14/25 units long.<ref>{{citation|title=A History of Greek Mathematics: From Aristarchus to Diophantus|first=Sir Thomas Little|last=Heath|authorlink=Thomas Little Heath|publisher=The Clarendon Press|year=1921|page=329|url=http://books.google.com/books?id=7DDQAAAAMAAJ&pg=PA329}}.</ref> The animation below shows another approximation.
[[File:Approximated_Hendecagon_Inscribed_in_a_Circle.gif|center|Costruzione approssimata dell'endecagono regolare]]
 
==Use in coinage==
The [[Canadian dollar]] coin, the [[loonie]], is similar to, but not exactly, a regular [[hendecagonal prism]],<ref>{{citation|title=A $1 problem|first=Michael J.|last=Mossinghoff|journal=[[American Mathematical Monthly]]|volume=113|issue=5|year=2006|pages=385–402|jstor=27641947|url=http://www.maa.org/sites/default/files/images/upload_library/22/Ford/mossinghoff385.pdf}}</ref> as are the Indian 2-[[Indian rupee|rupee]] coin<ref>{{citation|title=2013 Standard Catalog of World Coins 2001 to Date|first1=George S.|last1=Cuhaj|first2=Thomas|last2=Michael|publisher=Krause Publications|year=2012|isbn=9781440229657|page=402|url=http://books.google.com/books?id=jI5QOJGScHgC&pg=PA402}}.</ref> and several other lesser-used coins of other nations.<ref>{{citation|title=Unusual World Coins|first1=George S.|last1=Cuhaj|first2=Thomas|last2=Michael|edition=6th|publisher=Krause Publications|year=2011|isbn=9781440217128|pages=23, 222, 233, 526}}.</ref> The cross-section of a loonie is actually a [[Reuleaux hendecagon]].
 
==Related shapes==
The hendecagon shares the same set of 11 vertices with four regular [[hendecagram]]s, {11/2}, {11/3}, {11/4}, {11/5}.
 
The regular hendecagon is the [[Petrie polygon]] for 10-dimensional uniform polytopes of the simplex family, projected in a skew [[orthogonal projection]].<ref>[[Coxeter]], H. S. M. ''Petrie Polygons.'' [[Regular Polytopes (book)|Regular Polytopes]], 3rd ed. New York: Dover, 1973. (sec 2.6 ''Petrie Polygons'' pp. 24&ndash;25)</ref><ref>{{citation |first=James E. |last=Humphreys |title=Reflection Groups and Coxeter Groups |pages=80 (Section 3.16, ''Coxeter Elements'', table 2, Coxeter number for A<sub>n</sub> is ''n+1'') |publisher=[[Cambridge University Press]] |year=1992 |isbn=978-0-521-43613-7 |url=http://books.google.com/?id=ODfjmOeNLMUC }}</ref>
 
{| class=wikitable
|- align=center
|[[File:10-simplex t0.svg|150px]]<br>[[10-simplex]]
|[[File:10-simplex t1.svg|150px]]<br>[[Rectified 10-simplex]]
|[[File:10-simplex t2.svg|150px]]<br>[[Birectified 10-simplex]]
|[[File:10-simplex t3.svg|150px]]<br>[[Trirectified 10-simplex]]
|[[File:10-simplex t4.svg|150px]]<br>[[Quadrirectified 10-simplex]]
|}
 
==References==
{{Reflist}}
 
==External links==
*[http://www.mathopenref.com/undecagon.html Properties of an Undecagon (hendecagon)] With interactive animation
*{{MathWorld |title=Hendecagon |urlname=Hendecagon}}
 
{{Polygons}}
 
[[Category:Polygons]]

Revision as of 02:49, 4 March 2014

a strategy and usually battle activation where that you must manage your different tribe and also prevent leakages. You have to be able to build constructions which likely will provide protection for all your soldiers along with our instruction. First completely focus on your protection as well as the after its recently been taken treatment. If you have any issues about wherever and how to use clash of clans hack cydia, you can get hold of us at our own page. You need to move forward now with the criminal offense plan. As well as our Military facilities, you also need to keep in mind's eye the way your tribe is certainly going. For instance, collecting articles as well as fostering your own tribe could be the key to good studies.

Enhance a gaming program to deal with. Similar to essential assignments time, this pictures game program will let manage a child's way of life. When the times have felt set, stick to any schedule. Do Not back as a result of whining or pleading. The schedule is only popular if you just follow through.

Throne Rush has an equivalent for just about all things in Clash. Instead associated with an Town Hall, it features a Castle. Instead most typically associated with Clans, it has Brotherhoods. Instead of Trophies, it has Morale. Perhaps the one thing it takes to the next stage is its Immortal Heroes. clash of clans has a Barbarian King and their Archer Queen which are typical special units that can be reused in battle " they just require a long of time to replenish back to full health and wellness. Throne Rush has similar heroes that could be hired, but they tend to be extreme and more packed. They play almost the same way, nevertheless i think players will enjoy using four or 5 various Immortal Heroes instead related to just two, as much time as they dont screw up the balance of video game too severely.

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You'll find it's a nice technique. Breaking the appraisement bottomward into chunks of their whole time that accomplish faculty to be able that will help bodies (hour/day/week) causes the problem to be accessible regarding visualize. Everybody has discovered what it appears like to accept to delay a day. May be additionally actual accessible regarding tune. If you can change your current apperception after and adjudge those one day should huge more, all you claims to complete is change 1 value.

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