A key topic throughout school geometry is measurement--namely, distance, area, and volume. This article focuses on one key idea for finding and justifying the area of two-dimensional (2D) shapes: area-preserving transformations. Although especially pertinent to geometry teachers, this article highlights a vertical connection of ideas progressing…

The mean value theorem for differentials is basically a consequence of the fundamental theorem of calculus for Lebesgue integration.

Notes that the derivative of the area of a circle yields the circumference and the derivative of the volume of a sphere yields the surface area. Explores where these or other such relationships are generalizable. (PK)