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January 2006, Volume 99, Issue 5

FEATURES

Paper Moon: Simulating a Total Solar Eclipse
Sean Madden, James Downing, Jocelyne Comstock
This article describes a classroom activity in which a solar eclipse is simulated and a mathematical model is developed to explain the data. Students use manipulative devices and graphing calculators to carry out the experiment and then compare their results to those collected in Koolymilka, Australia, during the 2002 eclipse. Includes a description of how to set up the simulation and examples of student work.

Read how you can use this article as part of a Professional Development Experience.

Understanding Conic Sections Using Alternate Graph Paper
Elizabeth Brown, Elizabeth Jones
A description of two alternative coordinate systems and their use in graphing conic sections. This alternative graph paper helps students explore the idea of eccentricity using the definitions of the conic sections. Includes multiple examples of the uses of these alternative graphing sections, along with focus - directrix definitions of conic sections to be used with the new coordinate systems.

The Matrix Connection: Fibonacci and Inductive Proof
Tamara Veenstra, Catherine Miller
This article presents several activities (some involving graphing calculators) designed to guide students to discover several interesting properties of Fibonacci numbers. Then, we explore interesting connections between Fibonacci numbers and matrices; using this connection and induction we prove divisibility properties of Fibonacci numbers. Includes problems and samples of tasks used to help student discover patterns within the Fibonacci Sequence and connections to matrix algebra.

Using the Dynamic Power of Microsoft Excel to Stand on the Shoulders of Giants
John Donovan II
This article shows how Microsoft Excel's ability to vary parameters with sliders allows students to "stand on the shoulders of giants" and discover characteristics of polynomial functions. The article presents several problems and shows how they can be better understood from a graphical approach using Excel. Includes problems with possible solutions and follow up questions that lead students to an in-depth understanding of polynomials.

Finding Complex Roots: Can You Trust Your Calculator?
Barbara Ciesla, John Watson
This article investigates a specific instance when the textbook answer for finding a root of a complex number differed with the answer given by the TI-83. After explaining the reason for the difference the article then expands the definition of the integral root of a complex number to an arbitrary complex power of a complex number. Read now to see where false assumptions might be made based on the results of a calculator and see explanations of how to overcome those assumptions with logic and proof.