Trigonometric functions of radians for an integer not divisible by 3 (e.g., 40° and 80°) cannot
be expressed in terms of sums, products, and finite root extractions on *real* rational numbers because 9 is not a
product of distinct Fermat Primes. This also means that the Nonagon 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) |

The Discriminant is then

(7) |

There are therefore three Real distinct roots, which are approximately , 0.3240, and 0.6428. We want the one in the first Quadrant, which is 0.3240.

(8) |

Similarly,

(9) |

Because of the Newton's Relations, we have the identities

(10) |

(11) |

(12) |

© 1996-9

1999-05-26