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Hendecagon
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Hendecagon
In geometry, a hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon. (The name hendecagon, from Greek hendeka "eleven" and –gon "corner", is often preferred to the hybrid undecagon, whose first part is formed from Latin undecim "eleven".)
A regular hendecagon is represented by Schläfli symbol {11}.
A regular hendecagon has internal angles of 147.27 degrees (=147 degrees). The area of a regular hendecagon with side length a is given by
As 11 is not a Fermat prime, the regular hendecagon is not constructible with compass and straightedge. Because 11 is not a Pierpont prime, construction of a regular hendecagon is still impossible even with the usage of an angle trisector.
Close approximations to the regular hendecagon can be constructed. For instance, the ancient Greek mathematicians approximated the side length of a hendecagon inscribed in a unit circle as being 14/25 units long.
The hendecagon can be constructed exactly via neusis construction and also via two-fold origami.
The following construction description is given by T. Drummond from 1800:
Draw the radius A B, bisect it in C—with an opening of the compasses equal to half the radius, upon A and C as centres describe the arcs C D I and A D—with the distance I D upon I describe the arc D O and draw the line C O, which will be the extent of one side of a hendecagon sufficiently exact for practice.
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Hendecagon
In geometry, a hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon. (The name hendecagon, from Greek hendeka "eleven" and –gon "corner", is often preferred to the hybrid undecagon, whose first part is formed from Latin undecim "eleven".)
A regular hendecagon is represented by Schläfli symbol {11}.
A regular hendecagon has internal angles of 147.27 degrees (=147 degrees). The area of a regular hendecagon with side length a is given by
As 11 is not a Fermat prime, the regular hendecagon is not constructible with compass and straightedge. Because 11 is not a Pierpont prime, construction of a regular hendecagon is still impossible even with the usage of an angle trisector.
Close approximations to the regular hendecagon can be constructed. For instance, the ancient Greek mathematicians approximated the side length of a hendecagon inscribed in a unit circle as being 14/25 units long.
The hendecagon can be constructed exactly via neusis construction and also via two-fold origami.
The following construction description is given by T. Drummond from 1800:
Draw the radius A B, bisect it in C—with an opening of the compasses equal to half the radius, upon A and C as centres describe the arcs C D I and A D—with the distance I D upon I describe the arc D O and draw the line C O, which will be the extent of one side of a hendecagon sufficiently exact for practice.