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.

# Search Results

### 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.

### Øistein Gjøvik

An origami activity can lead to rich tasks in several branches of mathematics.

### Ron Lancaster

Rational functions and inverse variation underlie questions about fish tanks.

### Javad Hamadani Zadeh

Volumes of convex polyhedra are determined from constituent pyramids.

### Douglas Wilcock

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.