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## Reader Reflections – August 2013

Readers comment on published articles or offer their own ideas.

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## Finding Skewed Lattice Rectangles

Many mathematics instructors attempt to insert guided exploration into their courses. However, exploration tasks frequently come across to students as contrived, pertinent only to the most recently covered section of the textbook. In addition, students usually assume that the teacher already knows the answers to these explorations.

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## Geometry + Technology = Proof

Symbolic geometry software, such as Geometry Expressions, can guide students as they develop strategies for proofs.

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## Technology Tips: Exploring Three-Dimensional Worlds Using Google SketchUp

Google SketchUp is free, powerful and widely used Computer Aided Design (CAD) software that can have a transformative impact on the teaching of geometry. This article introduces Google SketchUp to readers through lessons that can be integrated into geometry classrooms and also provides additional resources for readers interested in learning more.

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## What's Inside the Cube? Students' Investigation with Models and Technology

Applying Zometool, vZome software, and The Geometer's Sketchpad to tetrahedrons nested in cubes enhances students' spatial visualization skills.

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## Mathematical Lens: A Mathematical Pyramid Scheme

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month, the photographs are of a pyramid in Egypt, and students are asked to compute volume, slant height, and the ratio of the base of the pyramid to its height.

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## Technology Tips: An Archimedean Walk

The circle, so simple and yet complex, has fascinated mathematicians since the earliest civilizations. Archimedes, a well–known Greek mathematician born in 287 BCE, began to unravel part of the mystery involving π by applying iteration to the circle. Building on Euclid's postulates and theorems, Archimedes used iterations of inscribed and circumscribed regular polygons to find upper and lower bounds for the value of π. These bounds are close approximations of the value of π, and one is still used today: 22/7 differs from π only in the third place to the right of the decimal (see fig. 1).