MATHEMATICIANS HOLD MEETING

At the first meeting of the Harvard Mathematics Club last night, Professor W. F. Osgood '86, Head of the Mathematics Department, spoke on the subject, "The Trigonometric Functions Treated Analytically."

In his talk, Professor Osgood brought out these points: "The trigonometric functions, sin x and cos x, are ordinarily defined by means of a right triangle; thus sin x equals a divided by c, etc. This procedure is natural, since the elementary facts of geometry appeal most strongly to our intuition.

"There are, however, other phenomena in physics of coordinate importance with those of geometry, namely, the phenomena of vibrating systems, of which the pendulum is a familiar example. The simplest type of oscillatory motion is governed by a differential equation of the second order, and two of the solutions of this equation are the functions sin x and cos x. By means of the differential equation the leading properties of these functions can be deduced with ease, and thus the foundations of trigonomemtry are laid."