I would say that the kaleidoscope is used to illustrate math calculations.
Suppose you looked into a special kaleidoscope and found a pattern that consisted of one object and seven images of that object. Can you figure out what the angle between the mirrors inside the kaleidoscope must be? You can experiment with your hinged mirrors, or you can use a mathematical formula to answer the question. Simply take the number of images you want, add one for the object itself, and divide 360 degrees by this number. Three hundred sixty divided by 8 is 45. So the angle between the mirrors must be 45 degrees.
http://musemath.blogspot.com/2007_03_01_…
Three mirrors, generally from four or five to ten or twelve inches long, and with a width of about an inch when the length is 6 inches, and increasing in proportion as the length increases, are put together at an angle of 60 degrees. With one mirror, an object is reflected such that the angle of incidence equals the angle of reflection... combining this with the mirror configuration above, a complex pattern forms between the mirrors due to the perspective of the eye looking down this long mirror shaft. The pattern forms with a real piece of glass seen in the actual opening at the end of the mirror. It is then reflected as seen below, and this complex pattern reflects outward yielding an illusion of an endless landscape of the glass piece. Below is the center most subset of the pattern.
http://the-hollander.com/math.html
Suppose you looked into a special kaleidoscope and found a pattern that consisted of one object and seven images of that object. Can you figure out what the angle between the mirrors inside the kaleidoscope must be? You can experiment with your hinged mirrors, or you can use a mathematical formula to answer the question. Simply take the number of images you want, add one for the object itself, and divide 360 degrees by this number. Three hundred sixty divided by 8 is 45. So the angle between the mirrors must be 45 degrees.
http://musemath.blogspot.com/2007_03_01_…
Three mirrors, generally from four or five to ten or twelve inches long, and with a width of about an inch when the length is 6 inches, and increasing in proportion as the length increases, are put together at an angle of 60 degrees. With one mirror, an object is reflected such that the angle of incidence equals the angle of reflection... combining this with the mirror configuration above, a complex pattern forms between the mirrors due to the perspective of the eye looking down this long mirror shaft. The pattern forms with a real piece of glass seen in the actual opening at the end of the mirror. It is then reflected as seen below, and this complex pattern reflects outward yielding an illusion of an endless landscape of the glass piece. Below is the center most subset of the pattern.
http://the-hollander.com/math.html