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March 2004, Volume 97, Issue 3

FEATURES

Tessellating the Sphere with Regular Polygons
Hortensia Soto-Johnson, Dawn Bechthold
Why spherical triangles, squares, and pentagons are the only shapes that will tessallate a sphere. Includes instructions for the tilings.

Fairness: How to Achieve It and How to Optimize in a Fair-Division Procedure
Michael Jones, Stanley Cohen
Three fairness criteria and an algebraic procedure that can be used to fairly divide items between two people. How an individual can use information about an opponent's preferences for disputed goods to maximize a return under the procedure, thereby introducing optimization without calculus.

Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid
Michael Brilleslyper
A standard approximation that uses simple quadratic equations to solve a problem in chemistry. The use of equation coefficients, the quadratic formula and inequalities to approximate solutions. Includes possible classroom uses.

The Constant Feature: Spanning K–12 Mathematics
James Schultz
How the idea of recursion and the constant feature available on calculators can be used to develop conceptual understanding. A variety of interesting and useful mathematical topics throughout the K–12 curriculum. Includes sample problems and solutions.