Thursday, February 17, 2011

math-art lesson plan: mandalas

Mandalas are a good way to teach about symmetry, concentric circles, diameters and angles. I wrote this lesson plan for next week's "Art in All Dimensions" class (after-school math/art combo).


creating a mandala – lesson plan

tibetan monks creating a mandala. source: a home away


introduction

Mandalas have existed in many cultures for centuries. They are an ancient and often spiritual art form. They are a symbol of integration, harmony and transformation. The most recognizable mandalas are from Tibet, where they are made as part of Buddhist practice, but mandalas have existed in many other cultures.

 source: daqui abalonya

Some say that the Druids built Stonehenge as a mandala, because it is formed around several concentric circles. 


 ptolemy's geocentric universe vs. copernicus' heliocentric universe. source: uc santa barbara

Early models of the universe (and of our own solar system) also look similar to mandalas. The different circles within a mandala can represent passing between different places or different dimensions.


activity
  • First, draw four or more concentric circles. What is a concentric circle, and what makes circles concentric? Leave some space between your circles to make some designs. In traditional Tibetan Buddhist mandalas, the concentric circles represent centering your energy. Buddhists believe that people have different types of energy that they release; drawing these circles helps to create a center point, and to “center” yourself while making it. This is an important part of meditation. Try to let your mind relax while you are drawing your circles, and make them whatever distance apart you feel like. Every mandala is supposed to be unique—different from any other mandalas. Try to make your own unique mandala, and don't worry about what your neighbor is doing!
  • Next, divide the circle up into four parts. What are the names of lines that go directly across a circle? How many of them do we have to draw in order to divide the circle into four parts? Draw these lines lightly, because you're going to erase them later.
  • Drawing these diameters creates four points on the outermost edge of your mandala. In many cultures, these represent or relate to the cardinal points of a compass – North, South, East, and West.
  • Why do you think we are dividing up the circle? The most important part of making a traditional mandala is that the parts of the circle are symmetrical. What does symmetry mean?
  • Next, draw one or more squares connected the edges of the circles. You can draw a small square in the center, or a large square between many circles. You can even draw a square around your whole mandala. Just make sure the points of your square hit the edge of one of your circles. In Tibet, Buddhist monks create mandalas with a square around the center of the mandala. This square represents where their deity—or god—exists.
  • You are now free to make designs and patterns within the small segments of your mandala. Try to repeat the same patterns in every section of the mandala, so that it will be symmetrical.
  • Once you've decorated your mandala with intricate shapes, you are free to color it in.




follow-up discussion & review

Where has the mandala pattern been found in history?

What does concentric mean? How about symmetry?

What are the points of north, south, east, and west called?

Were you able to understand why Buddhists consider creating mandalas an act of meditation? Were you able to relax your mind while making one? Why or why not?