Kaleidoscope by Number of Divisions

This kaleidoscope works by setting the mirrors to make a set number of sectors (pieces of pie) to divide the circle. The mirrors (reflecting lines) of the kaleidoscope are set on the edges of one piece, and then cause reflections in all the other pieces.

Try all the possible divisions from 1 to 12. What do you notice?

Are there any two division numbers that produce the same image? Why?

Are there any division numbers that don't make for a nice image? Why?

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What angle measures correspond to the different numbers of divisions? Show angles and find the pattern.

What makes a kaleidoscope image look good to you? Design an image that is cool to you. Describe what you like about it.

Posted at mathhombre.blogspot.com.

John Golden, Created with GeoGebra