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Harmonic Range

\begin{figure}\begin{center}\BoxedEPSF{HarmonicRange.epsf}\end{center}\end{figure}

A set of four Collinear points $A$, $B$, $C$, and $D$ arranged such that

\begin{displaymath}
AB:BC=2:1
\end{displaymath}


\begin{displaymath}
AD:DC=6:3.
\end{displaymath}

Hardy (1967) uses the term Harmonic System of Points to refer to a harmonic range.

See also Euler Line, Gergonne Line, Harmonic Conjugate Points, Soddy Line


References

Hardy, G. H. A Course of Pure Mathematics, 10th ed. Cambridge, England: Cambridge University Press, pp. 99 and 106, 1967.




© 1996-9 Eric W. Weisstein
1999-05-25