■正17角形の作図とガウスの公式(その28)
[2]式を書くだけでも大変なので,結果だけ書くと=√41−1
===================================
[2]cos2π/41+cos8π/41+cos18π/41−cos9π/41−cos9π/41+cos10π/41+cos16π/41−cos5π/41+cos2π/41−cos5π/41+cos4π/41−cosπ/41+
cos10π/41+cos18π/41−cosπ/41+cos20π/41+cos4π/41+cos8π/41+cos16π/41
+cos20π/41+cos20π/41+cos16π/41+cos8π/41+cos4π/41+
cos20π/41−cosπ/41+cos18π/41+cos10π/41−cosπ/41+cos4π/41−cos5π/41+cos2π/41−cos5π/41+cos16π/41+cos10π/41−cos9π/41+
−cos9π/41+cos18π/41+cos8π/41+cos2π/41=
−4cos(π/41)+4cos(2π/41)+4cos(4π/41)−4cos(5π/41)+4cos(8π/41)−4cos(9π/41)+4cos(10π/41)+4cos(16π/41)+2cos(18π/41)+4cos(20π/41)=√41−1
が得られた.
===================================