Exploring New Geometric Worlds

  • Exploring New Geometric Worlds

    Wayne Nirode
    Familiar sets of points defined by distances appear as unexpected shapes in larger-distance geometry.
    After my honors geometry students have studied Euclidean plane geometry, I like to broaden their conception to include different geometric worlds. One way is to have students explore a new way of measuring distance on the plane (e.g., taxicab geometry). When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds.
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