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・ Harmonic (disambiguation)
・ Harmonic (mathematics)
・ Harmonic analysis
・ Harmonic analysis (disambiguation)
・ Harmonic and Individual Lines and Noise
・ Harmonic balance
・ Harmonic balancer
・ Harmonic conjugate
・ Harmonic Convergence
・ Harmonic coordinate condition
・ Harmonic coordinates
・ Harmonic damper
・ Harmonic differential
・ Harmonic Disorder
・ Harmonic distribution
Harmonic division
・ Harmonic divisor number
・ Harmonic drive
・ Harmonic function
・ Harmonic Generator
・ Harmonic Grammar
・ Harmonic Inc.
・ Harmonic major scale
・ Harmonic map
・ Harmonic mean
・ Harmonic measure
・ Harmonic mixer
・ Harmonic mixing
・ Harmonic morphism
・ Harmonic motion


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Harmonic division : ウィキペディア英語版
Harmonic division
In geometry, harmonic division of a line segment ''AB'' means identifying two points ''C'' and ''D'' such that ''AB'' is divided internally and externally in the same ratio
:
\frac = \frac.

In the example shown below, the ratio is two. Specifically, the distance ''AC'' is one inch, the distance ''CB'' is half an inch, the distance ''AD'' is three inches, and the distance ''BD'' is 1.5 inches.
Harmonic division of a line segment is ''reciprocal''; if points C and D divide the line segment AB harmonically, the points A and B also divide the line segment CD harmonically. In that case, the ratio is given by
:
\frac = \frac

which equals one-third in the example above. (Note that the two ratios are not equal!)
The points ''A'', ''B'', ''C'', ''D'' divide the line harmonically as defined above precisely if the cross-ratio of the quadruple (''A'', ''B'', ''C'', ''D'') is 1.
Harmonic division of a line segment is a special case of Apollonius' definition of the circle.
==See also==

* Harmonic series (music)
* Projective harmonic conjugate

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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