Regular Hendecagon
Author
Eric W. Weisstein
Title
Regular Hendecagon
Description
The regular hendecagon is the regular polygon with 11 sides, as illustrated above, and has Schläfli symbol {11}. The regular hendecagon cannot be constructed using the classical Greek rules of geometric construction. The rim of the U.S. Susan B. Anthony dollar coin was a regular hendecagon, as illustrated above. The inradius, circumradius, and area of the regular hendecagon with unit side lengths are r = 1/2cot(1/(11)pi) approx 1.70284 (1) R = 1/2csc(1/(11)pi) approx 1.77473 (2) A =...
Category
Educational Materials
Keywords
URL
http://www.notebookarchive.org/2019-07-0z5jqsv/
DOI
https://notebookarchive.org/2019-07-0z5jqsv
Date Added
2019-07-02
Date Last Modified
2019-07-02
File Size
14.14 kilobytes
Supplements
Rights
Redistribution rights reserved
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Regular Hendecagon
Regular Hendecagon
Author
Author
Eric W. Weisstein
July 3, 2018
July 3, 2018
For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/RegularHendecagon.html.
©2018 Wolfram Research, Inc. except for portions noted otherwise
Figure
Figure
In[]:=
Graphics[{EdgeForm[Black],FaceForm[LightYellow],RegularPolygon[11]},ImageSize200]
Out[]=
Properties
Properties
RegularPolygonInformation[11]//TableForm//TraditionalForm
sides n | 11 | ||
vertex angle α {rad, degrees} |
| ||
central angle β {rad, degrees} |
| ||
inradius r | 1 2 π 11 | ||
circumradius R | 1 2 π 11 | ||
area A | 11 4 π 11 |
Inradius
Inradius
TraditionalForm[(RootReduce[RootReduce/@TrigToExp[Cot[Pi/11]/2]])]
(11264-42240+29568-5280+220-1)
10
x
8
x
6
x
4
x
2
x
10
N[r]
1.70284
Circumradius
Circumradius
TraditionalForm[RootReduce[RootReduce/@TrigToExp[Csc[Pi/11]/2]]]
(11-55+77-44+11-1)
10
x
8
x
6
x
4
x
2
x
10
N[%]
1.77473
Area
Area
TraditionalForm[RootReduce[RootReduce/@TrigToExp[Csc[Pi/11]11/4]]]
(1024-154880+6559168-113379904+857435524-2357947691)
10
x
8
x
6
x
4
x
2
x
10
N[%]
9.76103
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Cite this as: Eric W. Weisstein, "Regular Hendecagon" from the Notebook Archive (2018), https://notebookarchive.org/2019-07-0z5jqsv
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