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.
- Waring's Theorem
- Watchman Theorem
- Watson-Nicholson Formula
- Watson Quintuple Product Identity
- Watson's Formula
- Watson's Theorem
- Watt's Curve
- Watt's Parallelogram
- Wave
- Wave Equation
- Wavelet
- Wavelet Matrix
- Wavelet Transform
- Wave Operator
- Wave Surface
- Weak Convergence
- Weak Law of Large Numbers
- Weakly Binary Tree
- Weakly Complete Sequence
- Weakly Independent
- Weakly Triple-Free Set
- Weber Differential Equations
- Weber Functions
- Weber's Discontinuous Integrals
- Weber's Formula