A Kaleidoscope of Symmetry

When I was a kid, I used to be fascinated with these little toy telescopes. It was not a typical telescope, though. It was special because, when you took a peek through the lens, all sorts of flowers from far off places would magically appear and it would leave me breathless. Of course, now I know a little bit more about these so-called telescopes, also known as kaleidoscopes. A kaleidoscope is an optical toy that can be consisted of multiple arts and craft materials like a paper towel tube, mirrors, and colored beads, whose reflections produce changing patterns that are visible through the eyehole when the tube is rotated. The kaleidoscope was invented in 1816 by a Scottish scientist, Sir David Brewster, and patented by him quickly after in 1817. Brewster innovatively named his invention using Greek terms: kalos, eidos, and scopos—which when combined means the beautiful form watcher. The first kaleidoscope was made using old pieces of colored glass and other shiny objects, which are reflected by angled mirrors or glass lenses ultimately creating a pattern that can be viewed at the end of the tube. As time progressed, an American innovationist, Charles Bush took the kaleidoscope improved it immensely and turned it into a popular trend. He obtained patents for these improvements in 1873 and 1874, which were related to the further development of kaleidoscopes, kaleidoscope boxes, objects for kaleidoscopes, and kaleidoscope stands. Charles Bush, thus, became the first man to mass-produce kaleidoscopes in the United States of America. A kaleidoscope is a creation of many wonders but many people, such as my 5-year-old self, wonder how it works. Well, it’s easy! Every kaleidoscope should have four primary elements: the eyepiece, the body, the mirror system, and the chamber. Each of these elements plays a specific role. The eyepiece can be different shapes, sizes, and materials and allows the individual to view inside the kaleidoscope. The body, or the external housing, holds the contraption together. The mirror system determines the amount of mirrors used—two or three or even four. While the object chamber allows different materials to be viewed.
Though there are multiple characteristics found in a kaleidoscope, the way the mirrors are set up is the most significant element of a kaleidoscope. Variations of the kaleidoscope differ based on the mirror shape, the number of mirrors used, and the angle at which the mirrors are connected. Any variation of these three factors can and will produce numerous kaleidoscope images.
A kaleidoscope uses the mirrors or lenses within the tube to create reflections of anything in direct view of the end. The image reflected is considered symmetrical if the mirror is angled at an angle that is divisible by 360 degrees. For example, mirrors that are angled at 60 degrees create patterns of six regular sectors while mirrors that are angled at 45 degrees create patterns that create eight equal sectors and so on. The reason why these images can be considered symmetrical lies in its classification of its angles. A good kaleidoscope angle is one that creates a “star” pattern. That star has n “full” points that connect together at the point where two mirrors meet (without overlapping them) to form an overall pattern. Each n point includes a copy of the original design and its mirrored image. As mentioned previously, kaleidoscopic images are created diversely through its mirror system. There are many types of mirror systems that kaleidoscope creators use: the two-mirror system, the three-mirror system, the four-mirror system, the polyangular mirror system, and the tapered mirror system. Each system creates a different optical form. The two-mirror system, otherwise known as mandala, has three corresponding sides. Two of these sides are mirrors that create a “V” while the third side is blacked across the top. The angle of the created “V” determines the number of reflections that contain the image circle. When looking through the eyepiece, the pattern created makes a mandala. A mandala is the common single symmetrical snowflake.
The three-mirror system differs from the two-mirror system simply by using another mirror to close off the “V” shape the two-mirror system used thereby using three mirrors instead of two. There are four popular and common ways to assemble the mirrors. The first is called the equilateral triangle, which assembles the triangles into three equal sides and three equal 60-degree angles. The second is called the right triangle where no sides of the mirror are equal and no angles are equal. The third method, the isosceles triangle, allows two mirror sides to be equal with two equal angles. The last, the isosceles right triangle, has two equal sides and two equal angles with the third being a 90-degree angle. In the three-mirror system, images are reflected through out the entire image circle creating honeycomb patterns.
The four-mirror system is create when four mirrors are connected together to form three common shapes: square, diamond and rectangle. The square and rectangle shapes create two of the same patterns. These patterns are created by connecting the mirrors together at 90-degree angles, which, ultimately, causes the reflections to move up, down, left, and right. The pathway the reflections take creates a striped boxed pattern. The diamond assembly, on the other hand, creates images with multiple focal points. Somewhat similar to the two-mirror system, the four-mirror system creates a double mandala.
Polyangular scopes come in 2 or 4 mirror configurations. The 2-mirror polyangular scope is like the two-mirror system in that it uses two mirrors to create the “V” angle, however, with the polyangular scope, the variation lies in the ability to change the “V” angle thus changing the number of reflections and points. Most images that come through the eyepiece look like stars that can produce points anywhere from 2 to 30 points. The 4-mirror configuration is considered extremely rare. Producing a wide variety of images, the mirror configurations can change by shifting a square to a diamond. Thusly, the double mandala shape a 4-mirror system would create could produce square shapes as well.
The last but not the least of the mirror systems is the tapered mirror system. Tapering the mirrors allows the creator to angle the mirrors to create an isosceles trapezoid. If done correctly, the tapered mirror system creates a three dimensional image that is spherical in shape.
The two-mirror system, the three-mirror system, the four-mirror system, the polyangular mirror system, and the tapered mirror system all create such beautiful forms simply by tweaking the amount of materials used or by tweaking the placement of the mirror angles. These forms, when using a three-mirror system, can create forms of symmetry as well. A few ways to create symmetry are as follows: 1. Use the three-mirror system to combine the mirrors at 60-degree angles. This divides the circle into six symmetrical folds of continuous triangles. The number six stemming from the number of times a 60-degree angle is divisible by a full 360 degrees. 2. Use the three-mirror system to create an isosceles triangle where the mirrors form two 45-degree angles and one 90-degree angle. This creates a repeated diamond within a square pattern. 3. Use the three-mirror system to create a triangle with one 30, 60, and 90-degree angle. The 90-degree produces four folds while the 60 degree produces six folds, and the 30- degree produces 12 folds. Ultimately it creates a D6 figure repeated.
Now, what happens to a kaleidoscope when the angles of the mirrors do not evenly divide into 360 degrees? Odd angles produce continuous designs but only show partial images of the original image. Furthermore, the continuous designs of these partial images do not seamlessly merge together in a dissolving manner like the three-mirror system kaleidoscopes do. Kaleidoscopes are interesting contraptions that, if made correctly, produce beautiful symmetrical forms. There are multiple ways of constructing a kaleidoscope but, with the right idea and the right angles, any form is possible.
Works Cited
Baker, Cozy. Kaleidoscope Artistry. 2002. C&T Publishing.
Baker, Cozy. Kaleidoscopes: Wonders of Wonder. 1999. C&T Publishing.
Baker, Cozy. Kaleidoscope Renaissance. 1993. Beechcliff Books.
Baker, Cozy. Kaleidorama. 1990. Beechcliff Books.
Baker, Cozy. Through the Kaleidoscope…And Beyond. 1987. Beechcliff Books.