# Euclid's Muse

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# Whimsical Clocks Ch4 Kaleidoscope Clock

A Kaleidoscope works as a combination of reflections. Mirrors are typically arranged in an equilateral triangle producing multiple reﬂections as a symmetric pattern which changes as the triangle rotates. The apps in this collection explain how it's done, and then, of course, turn the kaleidoscope into a clock!

Tags: reflections, clocks, kaleidoscope

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#### Collection Contents:

##### Kaleidoscope clock
Here is our Kaleidoscope Click made with two triangles, the red one is the hour hand, the purple one is the minute hand.

Tags: Clocks, Kaleidoscope

##### Kaleidoscope
A kaleidoscope is typically made with  mirrors aligned as an equilateral triangle and rotated.  Multiple reﬂections form a symmetrical pattern which changes as the triangle is rotated. Drag the corners of the four original triangles to change the pattern, then drag the red dot to rotate the kaleidoscope.

Tags: Kaleidoscope, reflections

##### Combination of Reﬂections through Oblique Lines
Set the rotation angle and drag the center of rotation O so that the orange triangle sits on top of the image under the second reﬂection.  Can you describe another transformation equivalent to the two reflections?

Tags: reflections, rotations

##### Combination of Reflections through Parallel Lines
Press Reﬂect twice. Now drag point I so the orange triangle lies over the image under the second reﬂection.  Can you describe another transformation equivalent to the two reflections?
##### Reflection Clock
You can reﬂect the triangle in the minute hand, then reﬂect the reﬂection in the second hand.  How long does it take to do a complete rotation? You can change the triangle by dragging the red points.

Tags: clocks, reflections