
06455352
j
2015e.00762
Zazkis, Rina
Sinitsky, Ilya
Leikin, Roza
Derivative of area equals perimeter  coincidence or rule?
Math. Teach. (Reston) 106, No. 9, 686692 (2013).
2013
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
I44
G44
derivative
mathematical concepts
geometric concepts
volume
area
circle
sphere
square
polygon
Platonic solids
http://www.nctm.org/publications/article.aspx?id=36592
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 threedimensional figures  squares and regular polygons, cubes and regular polyhedra. (ERIC)