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Mandalas and Knot Designs

  • Background Information

    Mandalas are circular designs arranged in layers radiating from the center. Mandalas have been designed by Inca craftsman in the form of calendars and by Tibetan monks in the form of sand paintings.

    These sand paintings are rich in symbolisms and are used by the monks as sources for meditation. Mandalas are, by definition, rich in symmetries and therefore worthy of our own reflections. (No pun intended.)

    Knot designs are commonly seen in traditional Celtic art. Like the mandala, knot designs are by definition rich in symmetries. Knots are commonly shown as a single cord woven in and out of itself to form a symetrical design.

  • Assumptions and Definitions

    The author makes the following assumptions:

    • Access to a computer which is connected to the www through a browser such as Netscape. (Hey! you made it this far.)
    • The program: The Geometer's Sketchpad is installed onto the user's computer.
    • Netscape is configured to load Sketchpad as a helper application. Learn how to configure your browser to open sketchpad.

  • Students have a basic understanding of symmetrical terminology (i.e. reflection, translation, dialation)

  • Examples

    Here are some examples of mandalas.

    Visit these sources for further study of mandalas.

    Here are some examples of knot designs.

    Visit these sources for further study of Celtic knots.

  • Student Activities

    Download these sketches to see how to create your own mandalas and knot art.

    Make a Mandala with Sketchpad

    Example of a Seven Ring Knot

    Demonstration of Borromean Rings

    Learn to create more complicated knot designs.


    1. Create your own mandalas with Sketchpad
    2. Create your own knot design with Sketchpad
    3. What types of symmetries do you see in the previous examples?
    4. Locate the mirrors of reflection (if any) in each example.
    5. Locate the points of rotation (if any) in each example.
    6. Can you find the motif or basic unit which is being relected, rotated, dialated, or translated?
    7. Find corporate logos which use these same symmetrical concepts

  • Bibliography

    Send comments to: Rob Rumppe
    Created July 1996 Updated: 24 July 1996 A.D.

    Copyright 1996 by Robert Rumppe. All Rights Reserved