This paper presents a derivation of all five Lagrange points by methods accessible to sixth-form students, and provides a further opportunity to match Newtonian gravity with centripetal force. The predictive powers of good scientific theories are also discussed with regard to the philosophy of science. Methods for calculating the positions of the…

An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)

Among teachers of mathematics throughout the world there has recently been manifested a notable increase of interest in all educational work. This interest is due in part to the present general agitation in every educational line, in part to the influence of such related departments as physics, in part to the increased demands of industry, and in…