Geometry: Circular Billiards and Fractal Design

Circular Billiards

Circular billiards can be used as an entry point for students to discover the generalized inscribed angle theorem.
Inspired by Henri Picciotto’s Lab 1.9 on page 18 (PDF: http://www.mathedpage.org/geometry-labs/index.html) on the generalized inscribed angle theorem and N. Chernov and R. Markarian’s “Chaotic Billiards,” Preview available at: http://www.ams.org/bookstore/pspdf/surv-127-prev.pdf.

Fractal Design

Fractals are introduced with the hope that the geometry will be compelling and generative. Ultimately, students discover a relationship between scaling, copies and dimension for standard geometric objects and apply this relationship to understand features of fractals. Infinite series are also generated and explored.

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I am a math and science teacher at a boarding school in Delaware.

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2 comments on “Geometry: Circular Billiards and Fractal Design
  1. Very helpful, thanks for sharing!

  2. Peter says:

    Interesting knowledge, thank you!

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