Mathematical Lens uses photographs as a springboard for mathematical inquiry and appears in every issue of Mathematics Teacher. all submissions should be sent to the department editors. For more background information on Mathematical Lens and guidelines for submitting a photograph and questions, please visit http://www.nctm.org/publications/content.aspx?id=10440#lens.
Dustin L. Jones and Max Coleman
Many everyday objects–paper cups, muffins, and flowerpots–are examples of conical frustums. Shouldn't the volume of such figures have a central place in the geometry curriculum?
Linda L. Cooper and Martin C. Roberge
Let's go wading! Students connect fundamental mathematics concepts in this real-world, problem-solving field experience.
An origami activity can lead to rich tasks in several branches of mathematics.
Rational functions and inverse variation underlie questions about fish tanks.
Javad Hamadani Zadeh
Volumes of convex polyhedra are determined from constituent pyramids.
The sculpture Synergism, by William Severson and Saunders Schultz, is a stainless-steel structure exhibited in St. Louis (see photographs 1, 2, and 3). It is a series of three nested cubes in which the corresponding faces are parallel. The outer cube is punctured by three overlapping square-based prisms. The vertices of the square base of each prism are located at midpoints of the edges of the outer cube. A second cube attaches within the remaining structure and is similarly punctured, and a third cube attaches within the second and is punctured in the same manner. The outer cube measures approximately 4 meters on each edge. For the purposes of the following problems, we will use 4 m as the edge of the cube.
Cindy M. Cherico
Simulating a real-world marketing situation, students examine the mathematical calculations that play an integral part in product design.
Tongta Somchaipeng, Tussatrin Kruatong, and Bhinyo Panijpan
Students use balls and disks to prove the general formulas for sums of squares and cubes.
Rina Zazkis, Ilya Sinitsky, and Roza Leikin
A familiar relationship—the derivative of the area of a circle equals its circumference—is extended to other shapes and solids.