(Eq. 1) |

Geometrical construction to prove that arctan(1/3) + arctan(1/7) = arctan(1/2). (Rendered by the author using Inkscape). |

(Eq. 2) |

α | β | γ | _ | α | β | γ |

2 | 3 | 1 | _ | 15 | 98 | 13 |

3 | 7 | 2 | _ | 17 | 41 | 12 |

4 | 13 | 3 | _ | 18 | 47 | 13 |

5 | 8 | 3 | _ | 22 | 75 | 17 |

5 | 21 | 4 | _ | 23 | 30 | 13 |

6 | 31 | 5 | _ | 23 | 83 | 18 |

7 | 18 | 5 | _ | 27 | 46 | 17 |

7 | 43 | 6 | _ | 31 | 43 | 18 |

8 | 57 | 7 | _ | 33 | 76 | 23 |

9 | 32 | 7 | _ | 34 | 55 | 21 |

9 | 73 | 8 | _ | 38 | 47 | 21 |

10 | 91 | 9 | _ | 47 | 83 | 30 |

11 | 50 | 9 | _ | 57 | 68 | 31 |

12 | 17 | 7 | _ | 57 | 73 | 32 |

13 | 4 | 3 | _ | 70 | 99 | 41 |

13 | 21 | 8 | _ | 80 | 93 | 43 |

13 | 72 | 11 | _ | 83 | 23 | 18 |

(Eq. 3) | |

(Eq. 4) |

- Konstantine Zelator, "The Diophantine Equation arctan(1/x)+arctan(m/y)= arctan(1/k)," arXiv Preprint Server, March 28,2012
- Hasan Unal, "Proof without words: an arctangent equality," Mathematics and Computer Education, vol. 45, no. 3 (Fall 2011), p 197.