Radians Research Articles

Elementary Trigonometry

IN this volume the authors “have tried to recapture the spirit of some of the writers of a few generations ago who looked on Trigonometry as a branch of applied rather than of pure mathematics”. The course mapped out is therefore different in many ways from that found in most other textbooks. Great stress is laid on “the kind of calculations and manipulations of trigonometric expressions that occur in the applications of the subject”. Theory is not neglected, but it only enters where it is necessary to establish practical formulæ. The scope is fairly wide and includes an excellent section on mensuration and solid geometry. A welcome feature is the introduction of radian measure at the beginning.

The Definition of Radian

The Definition of Radian

“Steradians” and Spherical Excess

In elementary geometry, or oftener in trigonometry, we speak of radian measure of plane angles; but, if we ever mention the measure of a solid angle by the included area of a unit sphere, it is a mere comment, and seems to have nothing to do with the fact that the area of a spherical triangle is proportional to its spherical excess. It is not easy for the pupil to infer, and he generally does not infer, that the spherical excess, expressed in radians, is precisely this measure of the solid angle, and, if multiplied by r2, gives the area of the triangle.

Radian measures in plane-table mapping

Radian measures in plane-table mapping

The Word “Radian”

(1912). The Word “Radian”. The American Mathematical Monthly: Vol. 19, No. 10-11, pp. 166-166.

The Word "Radian"

The Word "Radian"

296. Approximate Construction for a Radian

296. Approximate Construction for a Radian