"Cyclotomic numbers and Chebyshev polynomials"의 두 판 사이의 차이

2017년 11월 19일 (일) 03:58 판

\[d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}\] satisfies \[d_i^2=1+d_{i-1}d_{i+1}\] where $d_0=1$, $d_k=1$

$$d_i = \frac{\sin (\pi (i+1)/7)}{\sin (\pi/7)} $$

Golden Fields: A Case for the Heptagon
- Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31

@@ 4번째 줄: / 4번째 줄: @@
 *  quantum dimension and thier recurrence relation
 :<math>d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}</math> satisfies
-:<math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math><br>
+:<math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math>
-#  (*choose k for c (2,k+2) minimal model*)k := 11<br> d[k_, i_] := Sin[(i + 1) Pi/(k + 2)]/Sin[Pi/(k + 2)]<br> Table[{i, d[k, i]}, {i, 1, k}] // TableForm<br> Table[{i, N[(d[k, i])^2 - (1 + d[k, i - 1]*d[k, i + 1]), 10]}, {i, 1,<br>    k}] // TableForm<br>
+==diagonals of regular polygon==
-#  Plot[d[k, i], {i, 0, 2 k}]<br>
+* length of hepagon
+$$d_i = \frac{\sin (\pi  (i+1)/7)}{\sin (\pi/7)} $$
-==diagonals of polygon==
-Clear[r]<br> r[i_] := Sin[((i + 1) Pi)/7]/Sin[Pi/7]<br> Table[N[r[i], 10], {i, 0, 5}]<br> Table[N[r[i]^2 - (1 + r[i - 1] r[i + 1]), 10], {i, 1, 4}]
@@ 26번째 줄: / 17번째 줄: @@
 * [http://pythagoras0.springnote.com/pages/4682477 체비셰프 다항식]
-* http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html<br> also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity<br><br>
+* http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html<br> also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity