Trigonometric functions of for an integer cannot be expressed in terms of sums, products, and finite root
extractions on *real* rational numbers because 7 is not a Fermat Prime. This also means that the Heptagon
is not a Constructible Polygon.

However, exact expressions involving roots of *complex* numbers can still be derived using the trigonometric identity

(1) |

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

(8) |

(9) | |||

(10) |

The Discriminant is then

(11) |

so there are three distinct Real Roots. Finding the first one,

(12) |

Writing

(13) |

(14) |

© 1996-9

1999-05-26