Difference between revisions of "Tridecagon"
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A '''tridecagon''' is a polygon with 13 sides. | A '''tridecagon''' is a polygon with 13 sides. | ||
| − | It has an internal angle degree of ~152.308 degrees and a total of 6840 degrees. The area is <math>A={\frac{13}{4}} a^{2} \cot {\frac{\pi}{13}}</math> which is about <math>13.1858 a^2</math> where <math>a</math> is the side length. This cannot be constructed by using a compass and straightedge, but can be constructed using an angle trisector or neusis. But, what if there's is not a side length value given? There is a formula for that too! The side length, where <math>r</math> is the radius of the circumcircle that this is being constructed on, of a tridecagon is <math>r \cdot 2 \cdot \sin{\frac{\pi}{13}}</math> or <math>2r \cdot 0.23931566428755777</math>. If this was constructed on a unit circle the side length would be <math>0.478631328575115</math>. The error of side length being off is 0.0 for up to 15 decimal places, so pretty accurate. If the radius was 1 billion km, then this formula would be off by lass than 1mm. The central angle of a tridecagon is about <math>27.6923076923077</math>, which is of by 0.0 degrees up to 13 decimal places. | + | It has an internal angle degree of ~152.308 degrees and a total of 6840 degrees. The area is <math>A={\frac{13}{4}} a^{2} \cot {\frac{\pi}{13}}</math> which is about <math>13.1858 a^2</math> where <math>a</math> is the side length. This cannot be constructed by using a compass and straightedge, but can be constructed using an angle trisector or neusis. But, what if there's is not a side length value given? There is a formula for that too! The side length, where <math>r</math> is the radius of the circumcircle that this is being constructed on, of a tridecagon is <math>r \cdot 2 \cdot \sin{\frac{\pi}{13}}</math> or <math>2r \cdot 0.23931566428755777</math>. If this was constructed on a unit circle the side length would be <math>0.478631328575115</math>. The error of side length being off is 0.0 for up to 15 decimal places, so pretty accurate. If the radius was 1 billion km, then this formula would be off by lass than 1mm. The central angle of a tridecagon is about <math>27.6923076923077</math>, which is of by <math>0.0</math> degrees up to 13 decimal places. |
==See Also== | ==See Also== | ||
* [[Polygon]] | * [[Polygon]] | ||
Revision as of 16:59, 7 June 2024
A tridecagon is a polygon with 13 sides.
It has an internal angle degree of ~152.308 degrees and a total of 6840 degrees. The area is 
which is about 
where 
is the side length. This cannot be constructed by using a compass and straightedge, but can be constructed using an angle trisector or neusis. But, what if there's is not a side length value given? There is a formula for that too! The side length, where 
is the radius of the circumcircle that this is being constructed on, of a tridecagon is 
or 
. If this was constructed on a unit circle the side length would be 
. The error of side length being off is 0.0 for up to 15 decimal places, so pretty accurate. If the radius was 1 billion km, then this formula would be off by lass than 1mm. The central angle of a tridecagon is about 
, which is of by 
degrees up to 13 decimal places.
See Also
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