Excerpt from The Texas Mathematics Teachers Bulletin, 1924, Vol. 11A less naive choice of a unit of angular measure is af forded in the radian. It partakes with the right angle of a certain inevitableness in its motivation but it has no astro nomical or constructional excuse for its selection. The ra dian is the angle subtended at the center of a circle by a circular arc whose! Length is equal to'the radius. A short discussion suffices to show that if this formulation of a definition be accepted as having a meaning in the case of a given circle, then the angle so defined is indeed definite and independent of the particular circle selected. A much more serious question is raised by the postulated comparison of the length of a circular arc with that of a rectilinear seg ment. This comparison will be accepted by most laymen without serious scruples, but is abhorrent to Euclidean purists. It can only be justified by a careful investigation of what is meant by length of an arc at least in this simple case, and by a general reliance upon the methods and con cepts of infinitesimal analysis. The radian, even after its definition is accepted, is found to be incommensurable with a right angle and hence with all of the other angles hitherto mentioned as units, and so is extremely awkward for many types of commercial computations. It has been adopted universally throughout the branches of higher mathematics, because of the simplification of the differential formulas involving the use of an angle that result from its intro duction. It is thus from the psychological viewpoint on a par with e, the celebrated base of Naperian logarithms.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.