@article {MATHEDUC.06455352,
author = {Zazkis, Rina and Sinitsky, Ilya and Leikin, Roza},
title = {Derivative of area equals perimeter -- coincidence or rule?},
year = {2013},
journal = {Mathematics Teacher},
volume = {106},
number = {9},
issn = {0025-5769},
pages = {686-692},
publisher = {National Council of Teachers of Mathematics (NCTM), Reston, VA},
abstract = {From the text: Why is the derivative of the area of a circle equal to its circumference? Why is the derivative of the volume of a sphere equal to its surface area? And why does a similar relationship not hold for a square or a cube? Or does it? In their work in teacher education, these authors have heard at times undesirable responses to these questions: ``That's the way it is. Circles and spheres are very special. Squares and cubes have corners.`` Or, ``It is a simple coincidence with circles. This relationship does not hold for any other shapes.'' In this article, we explore and explain the familiar relationship of the area of a circle and its circumference and of the volume of a sphere and its surface area. We then extend this relationship to other two- and three-dimensional figures -- squares and regular polygons, cubes and regular polyhedra. (ERIC)},
msc2010 = {I44xx (G44xx)},
identifier = {2015e.00762},
}