Century Dictionary and Cyclopedia
- Not harmonic; in geometry, a term applied by Chasles to an important kind of ratio introduced into geometry by Möbius. If a, x, y, b are four values of a unidimensional variable (for instance, the positions of four points on a line), then [(x—a): (x—b)] × [(y—b): (y—a)] is called the anharmonic ratio of the four values. The intersections of a plane pencil of four lines with a transversal have the same anharmonic ratio, however the transversal may be situated; and this ratio is called the anharmonic ratio of the pencil. Anharmonic ratios are always preserved in orthographic projections. By means of these ratios, metrical properties are defined as projective properties of the absolute, or conic at infinity. See
absolute, n., 2. If from the intersection of two lines tangents are drawn to the absolute, the logarithm of the anharmonic ratio of the pencil so formed multiplied by ½√—2 is the angle of the first two lines. So, the logarithm of the anharmonic ratio of two points, together with the intersections of their connecting line with the absolute, when multiplied by a constant, gives the distance of these points.
- adj. Not harmonic; perturbed harmonic.
GNU Webster's 1913
- adj. (Math.) Not harmonic.
- an- + harmonic (Wiktionary)
“Some of his works had a lasting effect on the whole development of statistical physics; I mean not only his study of the deduction of a "master equation" for anharmonic systems, but also his fundamental contribution on phase transitions, which was to lead to the branch of statistical mechanics that deals with so-called”
“This first study by van Hove was restricted to weakly coupled anharmonic systems.”
“Use the pendulum to find the value of g on planet X. Notice the anharmonic behavior at large amplitude.”
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