Geometric equivalents to changing rates

Abstract

Scope of Study: The teaching of the concepts involved in the study of acceleration and its effect on velocity and distance is difficult when working with students of general science and physics in high school, because their training in mathematics is necessarily limited by their ages. This study develops a method of solution of problems involving changing rates by the use of figures of reference having dimensions equivalent to the rates and constants encountered in the problems. The principles employed are similar to those used by Galileo and Descartes. The limitation of dimensions is overcome by reducing multiple dimensional figures to an equivalent line far use in representing figures requiring more than three dimensions. The development is by the use of simple drawings accompanied by explanations which require little more than the knowledge of the formulas for the areas and volumes of simple straight line figures, since the material is for high school use, and no attempt is made to proceed further than the derivation of a concept of the basis for the indefinite integral and the derivative.