Cyclotomic numbers and Chebyshev polynomials
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introduction
- borrowed from Andrews-Gordon identity
- quantum dimension and thier recurrence relation
\[d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}\] satisfies \[d_i^2=1+d_{i-1}d_{i+1}\] where \(d_0=1\), \(d_k=1\)
diagonals of regular polygon
- length of hepagon
\[d_i = \frac{\sin (\pi (i+1)/7)}{\sin (\pi/7)} \]
chebyshev polynomials
- 체비셰프 다항식
- http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html also obey the interesting determinant identity
articles
- Golden Fields: A Case for the Heptagon
- Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31