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Das regelmäßige Siebeneck besitzt einen Winkel von ( 360 7 ) o {\displaystyle \left({\frac {360}{7}}\right)^{o}} , das sind 51 , 428571 ¯ o {\displaystyle 51,{\overline {428571}}^{o}} , die dazugehörigen Winkelfunktionen sind daher transzendente Zahlen.
sin 360 7 ≈ 0.918032281143169... ≈ [ 0 ; 1 , 11 , 5 , 531 , 5 , 4 , 11 , 1 , 2 , 4 , 1 , 1 , 4 , 1 , 1 , 8 , 1 , 4 , 1 , 1 , 1 , 1 , 3 , 1 , 2 , 1 , 134 , 7 , . . . ] {\displaystyle \sin {\frac {360}{7}}\approx 0.918032281143169...\approx [0;1,11,5,531,5,4,11,1,2,4,1,1,4,1,1,8,1,4,1,1,1,1,3,1,2,1,134,7,...]}
11 12 ⋄ 56 61 ⋄ 29747 32403 {\displaystyle {\frac {11}{12}}\diamond {\frac {56}{61}}\diamond {\frac {29747}{32403}}}
cos 360 7 ≈ 0.396505650374707... ≈ [ 0 ; 2 , 1 , 1 , 10 , 1 , 5 , 1 , 1 , 6 , 18 , 1 , 1 , 1 , 12 , 2 , 2 , 2 , 1 , 1 , 18 , 1 , 8 , 1 , 3 , 1 , 1 , 1 , 1 , 3 , . . . ] {\displaystyle \cos {\frac {360}{7}}\approx 0.396505650374707...\approx [0;2,1,1,10,1,5,1,1,6,18,1,1,1,12,2,2,2,1,1,18,1,8,1,3,1,1,1,1,3,...]}
1 3 ⋄ 2 5 ⋄ 21 53 ⋄ 136 343 ⋄ 159 401 ⋄ 295 744 {\displaystyle {\frac {1}{3}}\diamond {\frac {2}{5}}\diamond {\frac {21}{53}}\diamond {\frac {136}{343}}\diamond {\frac {159}{401}}\diamond {\frac {295}{744}}}