Trigonometry Values Pi/17
Rather surprisingly, trigonometric functions of 
for 
an integer can be expressed in terms of sums, products, andfinite root extractions because 17 is a Fermat Prime. This makes the Heptadecagon aGauß. 
Although Gauss did not actuallyexplicitly provide a construction, he did derive the trigonometric formulas below using a series of intermediate variablesfrom which the final expressions were then built up.
Let
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Then
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There are some interesting analytic formulas involving the trigonometric functions of . Define
where
or 4. Then |  |  | |
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See also Constructible Polygon, Fermat Prime, Heptadecagon
References
Casey, J. Plane Trigonometry. Dublin: Hodges, Figgis, & Co., p. 220, 1888. Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 192-194 and 229-230, 1996. Dörrie, H. ``The Regular Heptadecagon.'' §37 in 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 177-184, 1965. Ore, Ø. Number Theory and Its History. New York: Dover, 1988. Smith, D. E. A Source Book in Mathematics. New York: Dover, p. 348, 1994.
- Bias (Series)
- Biaugmented Pentagonal Prism
- Biaugmented Triangular Prism
- Biaugmented Truncated Cube
- BIBD
- Bicentric Polygon
- Bicentric Quadrilateral
- Bichromatic Graph
- Bicollared
- Bi-Connected Component
- Bicorn
- Bicubic Spline
- Bicupola
- Bicuspid Curve
- Bicylinder
- Bidiakis Cube
- Bieberbach Conjecture
- Bienaymé-Chebyshev Inequality
- Bifoliate
- Bifolium
- Bifurcation
- Bifurcation Theory
- Bigraph
- Bigyrate Diminished Rhombicosidodecahedron
- Biharmonic Equation