Inversion

Inversion (Lat. invertere, to turn about), in chemistry, the name given to the hydrolysis of cane sugar into a mixture of glucose and fructose (invert sugar); it was chosen because the operation was attended by a change from dextro-rotation of polarized light to a laevo-rotation. In mathematics, inversion is a geometrical method, discovered jointly by Stubbs and Ingram of Dublin, and employed subsequently with conspicuous success by Lord Kelvin in his electrical researches. The notion may be explained thus: If R be a circle of centre O and radius r, and P, Q be two points on a radius such that OP·OQ = r2, then P, Q are said to be inverse points for a circle of radius r, and O is the centre of inversion. If one point, say P, traces a curve, the corresponding locus of Q is said to be the inverse of the path of P. The fundamental propositions are: (1) the inverse of a circle is a line or a circle according as the centre of inversion is on or off the circumference; (2) the angle at the intersection of two circles or of a line and a circle is unaltered by inversion. The method obviously affords a ready means for converting theorems involving lines and circles into other propositions involving the same, but differently placed, figures; in mathematical physics it is of special value in solving geometrically electrostatical and optical problems.

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