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

There are some interesting analytic formulas involving the trigonometric functions of . Define

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.

• Riemann-Christoffel Tensor
• Riemann Curve Theorem
• Riemann Differential Equation
• Riemann Function
• Riemann Hypothesis
• Riemannian Geometry
• Riemannian Geometry (Non-Euclidean)
• Riemannian Manifold
• Riemannian Metric
• Riemann Integral
• Riemann-Lebesgue Lemma
• Riemann-Mangoldt Function
• Riemann Mapping Theorem
• Riemann P-Differential Equation
• Riemann P-Series
• Riemann-Roch Theorem
• Riemann Series Theorem
• Riemann's Formula
• Riemann-Siegel Functions
• Riemann's Integral Theorem
• Riemann's Moduli Problem
• Riemann's Moduli Space
• Riemann Space
• Riemann Sphere
• Riemann-Stieltjes Integral