### Project Description

For my creative project, I decided to capture the mathematical topic of reflection through dance.

Essentially, I created a miniature music video to the song Mirrors by Justin Timberlake. The title of the song was quite fitting because I chose to use none other than the common household mirror to display the aspect of reflection in my project. With the help of a good friend and her novice videography skills, about seven mirrors of different shapes and sizes, and my dancing ability, I was able to aesthetically showcase the concept of reflection accompanied by Timberlake’s vocals.

The math behind how mirrors, meaning reflections, work is described by physics principles. Light is an essential aspect of reflection. The law of reflection explains how when light hits a surface it bounces back in a certain way, similar to a ball bouncing off of a wall. It says that the incoming angle of light, known as the angle of incidence, is always equal to the angle leaving or bouncing back from the surface, known as the angle of reflection. This is how reflection works. However, something I found interesting to ponder is that light itself is invisible until it bounces off something and hits our eyes. Meaning, a beam of light moving through space cannot be seen until it hits a surface. When the light beam runs into an object, the light is then scattered. This concept is called diffuse reflection and it represents how we see light when it hits an uneven

surface. The law of reflection is still present, but rather than the light hitting one even surface it is bouncing off of several microscopic surfaces. Because mirrors have a smooth surface, they don’t scatter light in this way. Instead, with a smooth reflecting surface, the light bounces off without disarranging the incoming image, which is known as specular reflection. This is why mirrors swap the image, turning it left to right and visa versa. A mirror image is a light-print of the image, not a reflection of the image from the perspective of the mirror.

Another aspect I wanted to focus on in my project is infinity in reflections. Meaning, whether two mirrors facing each other create infinite reflections. In my video, I tried to capture this aspect by holding up a mirror to another mirror to produce this infinite reflection looking effect. However, I learned that although they seem to create infinite reflections, it is not actually the case. The reflections get darker and darker and fade into invisibility long before they reach infinity. This is because mirrors absorb only a small fraction of the energy of the light striking them each time. There are never more than a few hundred visible reflections. Thus, when watching my video and awe-ing at the infinite reflections I had seemingly produced, remember it might not be as limitless as it appears. There is the wonderfully rhymed saying, “objects in the mirror are closer than they appear.” Perhaps, in regards to capturing infinity my music video, it should instead state, “although it appears this way to you and me, infinity is not, in fact, what we truly see.”

Of course, I also wanted my project to represent the aesthetics found in mathematics. I think dance is a very beautiful art form that has numerous connections to math. Although I wouldn’t say my project is an excellent example of aesthetic dancing, movement represents both mathematics and aesthetics. As with reflection, physics connects movement to math. Motion is the occurrence of an object changing positions over time and is thus mathematically connected to concepts and forces including velocity, displacement, distance, speed, acceleration, and time. Movement is math. Additionally, in hopes to make my video more aesthetically appealing, I wore green to match the grass and trees, and blue to reflect the sky. The bright colors in the background and reflected in the mirrors all contribute to portraying this appealing aesthetic. I wanted my project to display the mathematical aspect of reflection, but I also intended to make it enjoyable to watch. This is why I allowed my dog to make a special appearance. I think music, movement, and dance are brilliant ways to express creativity, but also to even exhibit more conceptual concepts. Mathematics and aesthetics are so much more interviewed than I think are initially presumed, and I hope my project was able to portray this beautiful connection.

### References

Matthews, Robert. “Do Two Mirrors Facing Each Other Produce Infinite Reflections?” BBC Science Focus Magazine,​ www.sciencefocus.com/science/do-two-mirrors-facing-each-other-produce-infin ite-reflections/.

Flinn, Gallagher. “How Mirrors Work.” ​HowStuffWorks Science​, HowStuffWorks, 27 Jan. 2020,

science.howstuffworks.com/innovation/everyday-innovations/mirror2.htm.

“Physics Tutorial: The Law of Reflection.” ​The Physics Classroom​, www.physicsclassroom.com/class/refln/Lesson-1/The-Law-of-Reflection.

“Mathematical Movement.” ​Mathematical Movement​, American Physics Society, physicsbuzz.physicscentral.com/2012/10/mathematical-movement.html.

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