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## Recreating History with Archimedes and Pi

Students use modern technology to investigate historical perspectives and calculate an approximation of π.

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## Teaching the Perpendicular Bisector: A Kinesthetic Approach

Through movement-a welcome change of pace-students explore the properties of the perpendicular bisector.

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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).

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## Voronoi Diagrams and Spring Rain

The same rain that washes out the high school baseball team's game supplies data for a class geometry project.

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## Geometry in Medias Res

Plunking students down in the middle of a geometry course—in medias res—helps them appreciate the axiomatic structure of geometry.

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Readers comment on published articles or offer their own ideas.

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## Tiles in a Circle

Photographs are a springboard for mathematical inquiry.

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## September 2016

A set of problems of many types

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## A New Recipe: No More Cookbook Lessons

Cookbook materials can be readily transformed into lessons that reflect a genuine inquiry approach.

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## Delving Deeper: Approximating π Using Similar Triangles

This article presents a method for approximating π using similar triangles that was inspired by the author's work with middle school teachers. The method relies on a repeated application of a geometric construction that allows us to inscribe regular polygons inside a unit circle with arbitrarily large number of sides.