ERIC Number: EJ1018066
Record Type: Journal
Publication Date: 2013-May
Reference Count: 3
Derivative of Area Equals Perimeter--Coincidence or Rule?
Zazkis, Rina; Sinitsky, Ilya; Leikin, Roza
Mathematics Teacher, v106 n9 p686-692 May 2013
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." This article explores and explains the familiar relationship of the area of a circle and its circumference and of the volume of a sphere and its surface area. It then extends this relationship to other two- and three-dimensional figures--squares and regular polygons, cubes and regular polyhedra.
Descriptors: Mathematics Instruction, Mathematical Concepts, Geometric Concepts, Equations (Mathematics), Teacher Education
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: firstname.lastname@example.org; Web site: http://www.nctm.org/publications/
Publication Type: Reports - Descriptive; Journal Articles
Education Level: Higher Education; Postsecondary Education
Authoring Institution: N/A