# construction of contraharmonic mean of two segments

Let $a$ and $b$ two line segments^{} (and their ). The contraharmonic mean

$$x:=\frac{{a}^{2}+{b}^{2}}{a+b}=\frac{{\left(\sqrt{{a}^{2}+{b}^{2}}\right)}^{2}}{a+b},$$ |

satisfying the proportion equation

$$\frac{a+b}{\sqrt{{a}^{2}+{b}^{2}}}=\frac{\sqrt{{a}^{2}+{b}^{2}}}{x},$$ |

can be constructed geometrically (http://planetmath.org/GeometricConstruction) as the third proportional of the segments
$a+b$ and $\sqrt{{a}^{2}+{b}^{2}}$, the latter of which is gotten as the hypotenuse^{} of the right triangle^{} with catheti
$a$ and $b$. See the construction of fourth proportional.

(The dotted lines are parallel^{}, with declivity ${45}^{\circ}$.)

Title | construction of contraharmonic mean of two segments |
---|---|

Canonical name | ConstructionOfContraharmonicMeanOfTwoSegments |

Date of creation | 2013-03-22 19:12:34 |

Last modified on | 2013-03-22 19:12:34 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 8 |

Author | pahio (2872) |

Entry type | Example |

Classification | msc 51M15 |

Classification | msc 51-00 |

Related topic | ContraharmonicProportion |

Related topic | HarmonicMeanInTrapezoid |