Comment on "On the geometry of parallel impedances"

In the original paper by S. Karni (see ibid., vol. 35, p. 233-4, 1992), the author argues that the time-honored custom of forbidding the use of angle-measuring devices in geometrical proofs appears to have been violated. If it were otherwise, the problem of trisecting an arbitrary angle would be trivial. Furthermore, the author states that the method proposed by Karni suffers from the disadvantage of employing one procedure for resistors and another for impedances. He argues that this is bound to prove awkward when then is a combination of the two. By far the most elegant geometrical method of handling impedances and resistors connected in parallel is that of inversion in a circle followed by reflection in the real axis. This requires that the impedances be given in rectangular rather than polar form. The author learned the inversion method (invented in the West at least a 100 years ago) in the 1950s as an undergraduate in his native India. In the modern age of computers, graphical methods can perhaps play a supplementary role.