Select three points at random on a unit Circle. Find the distribution of possible areas. The first point can be
assigned coordinates (1, 0) without loss of generality. Call the central angles from the first point to the second and
third and . The range of can be restricted to [0, ] because of symmetry, but
can range from . Then

(1) |

(2) |

(3) |

(4) |

But

(5) |

Write (4) as

(6) |

(7) |

(8) |

(9) |

so

(10) |

(11) |

so

(12) |

(13) |

(14) |

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1999-05-26