Objects Warped by the Shape of Glass, Liza Richards

Project Description

For my creative project, I chose to demonstrate through photography how transparent glasses filled with water warp the appearance of the object behind them when looking through the glass. Differently shaped glass warps objects in a variety of ways. They may cause the appearance of the object to be smaller, larger, stretched, twisted, magnified, etc. The photograph I produced is designed to show exactly this and highlights their differences. While taking this photo I chose to use as plain of a background as I could find to emphasize the true focus of the photograph, the glasses and the distortions of the objects behind them. In order to make the ground more plain, I placed down pieces of blank white paper to avoid the patterns on the ground to take away from the flowers on display. I placed 7 flowers of different shapes, sizes, and colors behind the 4 glasses to use as the objects to be warped by the glass. My initial set up plan was to place each flower directly adjacent to one another, but I quickly figured out that with the ways the glasses warped the shapes, some of the flowers were not reflected through the glasses. To fix this, I had to move some flowers farther away from the others so that they would actually be seen through the glass which you can see with the photos I provided of the set up and the flowers without the glasses in front of them. I also struggled with the angles at which to take the photograph. I provided two somewhat different views of the glasses to allow the viewer to see how the angle at which you view the glasses changes the shape of the objects as well. You may notice that the the outermost right glass is the one that changed the appearance of the flowers the most with the different angle.

When comparing the photograph of the original flowers to the one of them behind the glasses, it can be observed that the flowers in the glass on the far left are pushed to the left side of the glass more and appear to have shrunken a little. This is due to the convex shape and curve of the glass. In the tallest glass, it is seen that there are actually two images of the same flower reflected in it. The one on the top is the same as the bottom except it has been flipped upside down. This is due to the concave curve of the glass near the top. In addition, the lower concave curve leads to the lower flower being shrunk. The glass in the middle right has multiple edges and corners, leading to multiple different refractions of the same flower through each section. The glass on the farthest right has an octagonal pattern engraved the glass while being concave and therefore magnifies and bends the flower into a combination of octagonal shapes.

We use glass in a multitude of ways similar to how they are used in this photograph. It is used in magnifying glasses, binoculars, and microscopes to allow the viewer to have a close up view of what they are observing. The way the curves of the glasses change the shapes of the flowers can also be seen in fun house mirrors, where the shape of the mirror warps the image reflected off of it. For these reasons, this photograph has mathematical connections to geometry, optics, and refraction.

Geometry is concerned with the properties of surfaces, solids, lines, etc. Geometry is an important part of mapping like navigation and astronomy. It can also be used in animations and designing. The geometry of the glasses changes how the object is viewed through the glass. The convex or concave curves will effect if an image is magnified or shrunk. The shapes in the glass lead to the object to be distorted to fit those same shapes as well. In addition, the appearance of the object through the glass depends on the original geometry of the object as well. Each of the different geometries present in these glasses changes the appearance of the object in their own unique way.

Optics is the study of sight and behavior of light and deflection. The geometry of the glasses deflects the original object, changing the appearance of the it in multiple different ways. The sole change in the appearance itself of the object through warped glass involves the study of optics. The study of optics is most known in our society through the creation of contact lenses and glasses to allow better eyesight. When we view the object through the water filled glasses, we are studying optics because we are observing how the image of the object changes as it is deflected through the glass.

Refraction is the phenomenon of light and objects being deflected in passing through an interface. It is mostly seen in rainbows, camera lenses, and binoculars, all involving how light is reflected and seen. When taking the photograph, I tried to avoid as much outside light as possible in order to allow only natural light to effect the appearance of the object. The deflection of the object can be considered a part of refraction. The natural light shining through the glasses allows the object to be warped in the way that it is. As the light passes through the glass, the portrayal of the object behind it changes.

In conclusion, as light shines through the water filled glasses, the shape of the glass effects the appearance of the flowers viewed through the transparent glass. The convex and concave shapes in the glasses shrink or magnify the flowers behind them. The edges and shapes in the glass lead to different distortions of the flowers through the glass. The changes in the appearance of the flowers are a result of the geometry of the flowers and the glasses, the optics and how the appearance of the flowers changes through the glass, and the refraction of light through the glass changing the shape of the flowers in the first place. A combination of these different types of mathematics is what explains the altered appearance of the flowers resting behind the glasses.


The Path of a Frisbee, Carmen Resnick

The project I will conduct will observe the path taken by a frisbee in flight from a “backhand huck.” There are two facets to my project, the aesthetics of the path taken and the math behind the aerodynamics of a frisbee. 

A backhand huck is used in ultimate frisbee at many of the most vital times in a game. An official game of ultimate frisbee begins with a “pull” where the frisbee is sent from one end of the field to the other by the defending team. Often, a backhand throw is used for this because it is the easiest to put enough power behind using the rotation of the torso and hips. To throw a backhand, the thrower steps with their dominant foot across their body and the disc starts at the non-dominant side. This movement will be demonstrated in the final project through a visual presentation. 

In a study done by Kathleen Baumback at the University of South Florida in 2010, the path of a frisbee was recorded in relationship to its initial angle. A series of calculations and formulas was used to understand the aerodynamics of a frisbee. Frisbees have multiple elements of their shape, as well as components such as spin, that enable them to maintain “lift” after the disc has left the hand of the thrower. This experiment was done to reproduce a similar study in 2005 which sought to “predict the path of a frisbee” (Baumback 3). This study recognizes the mathematic derivations to determine how the angle of initial release impacts the forces of lift and drag on the frisbee’s flight. All calculations and determinations were done through Java programming. 

The mathematics in my project are tailored more towards the aesthetics of a frisbee’s flight rather than the practicality of predicting it. I am interested also in taking the derivative of the determined graph (if possible) to understand the change in the frisbee’s angle over time. Two graphs will be created, one is similar to Baumback’s study of distance where the height reached by the frisbee will be observed over time and the other will study the angle of the disc with respect to the ground. 

Though not mathematically profound, this project serves to represent the beauty of seeing mathematical concepts in practice. Much more research could be done to comprehend how and why the physical shape and size of a frisbee impacts its flight. Additionally, the visualization of how a disc moves through the air will provide some clarity for me as a thrower to understand the disc’s momentum. 

There are many variables that influence the graphing of a frisbee in flight, both in the movement of the frisbee as well as the camera set-up and post-filming production content. I will video a frisbee in flight, ensuring that the camera is positioned behind the thrower. The angle behind the thrower will show the angle of the disc with relation to the ground, and the camera will be set up in a way that ensures that the bottom of the screen is parallel to the ground. From this angle, I will record both the degrees of inclination from the horizontal at various points in time, as well as the height of the disc from the ground. 

The original plan to observe the distance traveled by the disc was thrwarted when we took to the fields and realized that the disc’s distance would be impossible to capture in one frame of a video, and similarly difficult to measure on a screen. The height measurement is still accurate with regards to the screen because the camera was set up perfectly perpendicular to the ground.

Data and Methodology

Works Cited

Baumback, K. (2013). The Aerodynamics of Frisbee Flight. Undergraduate Journal of Mathematical Modeling: One + Two, 3(1). doi:10.5038/2326-3652.3.1.31


untitled, Laurel O’Brien

In geometry, regularity is often given great value, since it makes things simple and easily comprehensible. The symmetry and regularity of polygons tends to translate there into an aesthetic value. For this creative project, the main concept was to take an interesting 3-D shape drawn in 2-D, and change it by applying to it the idea of limits and to make it irregular, but still beautiful. The inspiration for this project was simply the curiosity and desire to look at and tinker with an interesting shape and take aspects of both the geometric and the calculus and mash them together into their own aesthetic fusion. Essentially, I wanted to do project synthesizing mathematical representations with the medium of embroidery, using an increasing number of stitches per sector of the structure going counter-clockwise. The desired effect was that it would slowly become more circular, the number of stitches increasing and more and more compressed in the manner of the values of a curve approaching a limit or bound. 

The shape in question that I tinkered with is best described as a sort of 3-D hexagonal mobius strip, a structure that folds in on itself endlessly. In the drawing I found, it looked almost Escher-esque (we then covered Escher much later in the term), and studying it, I found that the 2-D representation, being quite hexagonal in nature, could be split up into six primary sectors. It has six arms spiraling out from the center, six inner corners, and 12 sides made up of 18 congruent lengths. To construct the sectors, then, two sides, or 3 of the congruent lengths, would comprise each sector. Taking that into account, the congruent lengths within each successive sector would each have an additional stitch than those in the last, meaning that the stitch count for the outer border would increase per sector by 3 ( (#of sector)*3= sector outer border stitch count). Using this, I overlaid a circle onto the outer border and then plotted points on the circle, split the sector of the circle for each congruent length into its allotted amount of stitches. Then, for the spiraling sections, I took the spiral that operated largely within a sector and paired them, overlaying a circle onto each one, and giving each congruent length the same number of stitches as the outer and inner borders of its sector. These would have the result of creating an increasingly circular shape going around the structure counterclockwise.


Unfortunately, the complexities of the pattern turned out less visible as I had hoped. First, I think the shape, already being hexagonal, did not leave much room for a visual comparison between angularity and circularity. Had I done this with a similar structure that was pentagonal, the results might have been more satisfyingly defined. Since the idea is to make the irregular beautiful, I had hoped to make the irregularity of its shape clear, because if it had a clear pattern, it could simultaneously be irregular and retain a sort of regularity in that pattern. 

The project as a whole was a bit of a battle for visibility. I switched from white cotton fabric to painted black canvas to ensure that stitches would stand up and pop out from the embroidered medium, and had used 12-count (an homage of sorts to the recurring theme of base 6) white thread to try and bolden the outlines and raise the ends of the stitches away from each other. I wanted to make each individual stitch clearly defined and countable. I used four shades of green thread to shade the spiraling sections, trading thick 12-stranded thread for 3-stranded thread to try and keep the shaded areas (which ended up meaning a bit more than four times the stitches overall for smooth coverage). Also, I settled on green for the color of the shading after our unit on color theory, wanting to keep the color itself one of the base three, and when I had digitally prototyped the different colors, it looked much more natural than blue or red (In retrospect, this was probably subconsciously due to the existence of the wreath). Using red thread, I also made six French knot points on both the inner and outer borders of the structure to visually help separate and contain the individual sectors, twelve points in total. Despite these attempts for clarity and visibility, things ended up less defined than I would like. Working with painted canvas embroidery for the first time, I did not expect that each time a hole was poked in the canvas, the rupturing canvas would bring back up the white underside, making things messy. So, after all of this, what I seem to have created, visually, is a mathematical wreath with mathematically-placed berries. Perhaps, if we were ever able to display our works in a room on campus somewhere, we could hang it on the door.


Patterns and Symmetries in Music, Chloe Miller

For my project I did a video presentation about the patterns and symmetries within music, specifically focusing on musical fractals. I decided this format was best so I could share both my own musical fractal as well as already existing musical fractals that exist in other composers’ music. While my video itself contains much of the mathematical overlap and main ideas I learned I will take the space here to write down both things said in the video, as well as things that I learned in the process of creating my project.

To start I’ll explain what a fractal is. A fractal consists of patterns that build off of one another to create something more complex and beautiful. Below this is a picture of a pythagorean tree fractal. Here we see it starts with a square, then there are two more squares added, then to each of those two more, and this pattern continues on and on.

A musical fractal, as I explain in the video, is some sort of property about the music whether that be a rhythm, tension, pitch, or something else that is a part of a bigger picture and is building off of other dynamics within the music to create this musical fractal. It can also be described as a symmetry or pattern found within music. One composer who was a master at using musical fractals was ​Johann Sebastian Bach. Many of these musical fractals occur within his canons, which makes sense since canons themselves have many fractal-like properties of starting with a melody then creating different variations of that melody at different speeds, styles, instruments, or even different keys.

In my project I wanted to be able to show these fractals in a way that helped the listener be able to visually see the patterns as well as hear them. To do this I found a program called Music Animation Machine (MAM) created by Stephen Malinowski. This app took audio files and created visualizations of the music from abstract images to lines and dots scrolling across the page (this was the visualization I used in my video presentation). Each series of lines and dots represents a different instrument part and in my presentation I showed the example of Bach’s Brandenburg Concerto #4, movement 3. Each note is represented by a dot and the lines are there for fluidity, duration, and aesthetic purposes. As the video plays there are numerous patterns and symmetries we can see. We notice similar melodies and themes occur and bounce around from instrument to instrument.

Finally at the end of my video presentation I showed my own original composition of a musical fractal. I tried to incorporate the same melody in different octaves as well as note lengths. Instead of simply summarizing the video I wanted to explain what I learned during this process and really a key take away I got from this project. After I had spent countless days and hours trying to make my musical fractal composition at least not sound awful, I began to realize that to create symmetries and fractals in music is something that can not be done by anyone, but is a skill that takes expertise in many disciplines to be able to create something that actually sounds beautiful and aesthetically pleasing. Bach was successful in his compositions of musical fractals because he understood both mathematics as well as music and how to incorporate them both to create something amazing. Bach not only relied on the calculations and math to create his music (like I mainly focused on), but he also understood that audiences don’t simply want to hear something completely predictable. Music is a creative process because of its originality; the way Bach uses not just mathematics to create his music, but also the element of surprise and other musical qualities makes Bach’s music authentic and beautiful.


DancingPhilosopher. ​Animation of an Imperfectly Self-Resembling Pythagoras Tree​. 16 Oct.

2019,en.wikipedia.org/wiki/File:Animated_self-resembling_Pythagoras_tree_(fractal).we bm. Accessed 3 June 2020.


Lucas, Meagan McCoy

Puzzle piece trees
in sunlight through their leaves
seem at home among bumblebees.
Near bulbs with roots tangled in dirt sipping water from soil,
blooms speak in codes of bright hue; cyphers of light refracted
'cross retinas transcribe the waves
from nature and numbers
vibrant color

For my math project, I decided to write a poem using the Lucas number sequence to determine the number of feet per line, where a foot is a pair of syllables. Once I reached seven feet I decided to repeat the sequence backward, reversing the form to create a horizontally symmetrical shape with two distinct halves.

Usually, poems will use feet that follow a particular rhythm of stressed and unstressed syllables. I did not pay particular attention to the rhythm of my poem, but it might have some kind depending on how people choose to read it. I attempted to use an iambic meter in the beginning, but the constraints brought by the form of the poem made it difficult to implement any other attributes.

For the content of the poem, I tried to draw on what we learned in class, and what my attempts at gardening have taught me. The first half focuses on flora, while the second half is on the concept of light. I’m not sure who scientifically accurate my description of light is, but it was inspired by our reading on rainbows. I thought it was interesting how light, as we know it, is a phenomenon that really only happens in our brains. Without someone to observe, the waves of light are not really color. This is interpreted in my poem as a form of communication, and translation. Without someone to observe, a flower is not really red or purple, and it is not pretty/aesthetically appealing either. Color then can be understood in two ways, mathematical or scientific analysis, shown by waves, or through experience through the senses, what we know as color. The path of the light waves from the flower to the eye in the second half of the poem means to synthesize these aspects. By understanding the miraculous nature of light and its interesting mathematical properties we can better appreciate its beauty.

The Lucas numbers sequence begins with two and one, and are added to produce the next number in the sequence, where the new number is always the summation of the last two numbers. For my project, I only went up to seven, but I explored the sequence before starting the poem. Up to seven, where this property seems to break down, you can take the values of each number in the sequence, make each individual number an area, and make a rectangle out of the Tetris-like pieces. I am not sure why it stops working at seven. It seems that it was just a coincidence, but I am sure that it works at least once more further down the sequence. The Lucas series is similar to the Fibonacci sequence in that it makes a spiral, but the Fibonacci sequence is more famous. The spirals produced look nearly the same, so I wonder if the Lucas series is found in nature as often. I am not sure I can spot much difference between the spirals visually, so there might be other factors that led to the reputation of the Fibonacci sequence. The pattern of summation between the two series is the same, but they just start with different numbers: one and one, and one and two, for Fibonacci and Lucas respectively. I have not looked into the timeline between when these sequences were discovered or rather invented, and if the Lucas numbers were more modern comparatively, which might explain the difference in their reputation.

Overall, I think I was successful in producing an art piece that really engages with the material. I used mathematical content and form, which we looked at in our reading, and I thought about aesthetics in a meaningful way. I have learned quite a bit from this project, and I feel that the form of the poem both enhances its content, and forced me to write in more creative ways, really appreciating every syllable I used.


Warped Perspective, Amelia Hamerlynck

Warped Perspective:

a Mathematical and Aesthetic Journey with the Fisheye Lens

In 1906, optical physicist Robert W. Wood wanted to invent a lens that would show the world from the perspective of a fish, “whose view from underwater compresses the entire horizon” (Vox). His paper discussed an experiment involving “a camera in a water-filled pail starting with a photographic plate at the bottom, a short focus lens with a pinhole diaphragm located approximately halfway up the pail, and a sheet of glass at the rim to suppress ripples in the water” (Vox). The resulting fisheye lens might have remained a novel item of early photography consigned to oblivion, but instead it took on a life of its own as fisheye lenses became commercially available in the 1960s. The fisheye’s multipurpose style has proven successful and popular from the lens’s first prototypes to modern smartphone apps.

While viewing the world from the eyes of a fish may seem a peculiar goal for a physicist, Wood’s work was both a natural outgrowth of early experimentation with a relatively recent invention and highly important in furthering our understanding of light. His other inventions, from a “disk whose microscopic experiments helped determine the age of stars” to infrared photography often used in nature documentation and thermodynamics, have occupied realms of physics without influencing the art world as strongly (Vox). The fisheye lens, then, is that unique instance of math meeting pop culture. I attempted to showcase this phenomenon in my project by explaining how each image represents a unique ability of the fisheye lens to interpret the world around us, interspersed with math, physics, and scientific history lessons on how and why the fisheye lens works.

The mathematical qualities that create the fisheye mainly involve manipulation of angles, distortion, and perspective. Rectilineal lenses represent straight features as straight lines. Distortions, therefore are deviations from rectilineal projection (Wikipedia). Fisheye lenses are extremely wide, massively distorting their subject matter and creating an illusion of convexity or concavity. The result is either hemispherical, meaning all the points in the image appear to be of

equal distance from the center; or panoramic, conveying a massive scale using wide angles (Wikipedia). In other words, widest highest quality fisheye lenses will capture absolutely everything from objects directly to their left to directly to the right of the lens; some are so wide one can take a photograph of a ceiling and capture the floor (Brownlee). “While wide-angle rectilinear lenses can capture angles of view approaching 100 degrees, fisheye lenses can stretch that to 180 degrees — impossible to do without the light bending science they employ” (Cunningham). In principle, this occurrence is simple refraction, the bending of light as it changes medium, just as one sees upon placing a pencil in a glass of water, hence the connection to a fish’s worldview and the usage of water in Wood’s experiment (Hashem). “The tradeoff is distinct: Straight lines anywhere but dead center in the fisheye image appear to curve. The farther they are from center, the greater the curved distortion” (Cunningham). So, whether one reenacts Wood’s experiment with light and water; utilizes an actual fisheye lens, which functions because of its physical shape; or, like me, takes photos using an app created by computer code; the origins of the fisheye’s instantly recognizable aesthetic is deeply rooted in mathematics.

Many of its applications are scientific. In nature, landscape, astronomical, and meteorological photography, the fisheye lens is uniquely qualified to capture both tiny spaces and huge spaces. Astronomers have therefore used it to photograph both the surface of mars and the movement of stars, as well as the confined quarters of a space vessel (Vox). I unfortunately did not have access to this subject matter, so instead I juxtaposed my use of the fisheye to capture me in my bathtub to my feet dangling over a cliff at a lookout point. My photographs of trees are meant to mimic the fisheye’s portrayal of the sky as a dome rather than a vast expanse.

Of course, many common usages of the fisheye are probably completely unaware of the lens’s mathematical origins, but they nonetheless make unique use of mathematical phenomena. Countless album covers from jazz to hip hop have utilized the lens to make artists appear larger-than-life. It helped that the release of the first consumer-grade fisheye lens in 1962 roughly coincided with the advent of rock ‘n’ roll and wider youth culture (Vox). The fisheye’s ability to distort made it instantly popular among the psychedelic rock stars of the 1960s including the Birds and Jimi Hendrix, who worshipped everything surrealistic and trippy. 1990s skaters filmed countless videos with the lens to properly capture the curves and swerves of a skatepark, one invention of optical physics capturing another invention of motion physics. I attempted to pay tribute to both art movements with my fake album cover photographs. And, of course, harkening back to Wood’s original intent, fisheye lens photos of my dog’s face represent the last thing a fish sees before being eaten.


Brownlee, Marques. “What is a Fisheye Lens?” YouTube. November 30, 2011.

Cunningham, Matt. “What is fisheye lens photography?” HowStuffWorks.


“Fisheye lens.” Wikipedia, the Free Encyclopedia. https://en.wikipedia.org/wiki/Fisheye_lens

Hashem, Amin. “What Is Fisheye Lens – The Full Guide.” Ehab Photography. May 11, 2018.

“How the fisheye lens took over music.” Vox. YouTube. Film. December 17, 2019.


Movement and Mirrors, Frida Graumann

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.


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,


“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.


untitled, Stella Feuerborn

Project Description

When we were first told of the guidelines for our final project, my mind went to graphs.

Graphs, linear graphs in particular, have always helped me to better understand the math I was working with. They have created visual representations of data I couldn’t previously visualize, and helped me see clearly what I was working with. I also feel like they’re a form of math that has been pretty universally worked with, and therefore would make my project more accessible. Once I had the idea graphs, I needed a way to display them in an artistic medium. Photography is a field I’ve been working for about 3 years now, and using the human body as an art medium is a powerful form of symbolism. So, I landed on the project I just finished.

For my project, I chose to depict 5 common graphs through photography with environmental elements and the human body. The sign post and curb acted as my x and y-axis. Then, I positioned the model (the lovely Carmen) at the visual intersection of these two lines, and had her shape her body to resemble graphed lines. The five graphs I chose to show were:

= |x| , and sin(x).

After taking the photos and color-correcting them, I drew a digital axis and where the rest of the graph would’ve gone beyond the figure.

From start to finish, this project ended up going beyond just the representation of graphs in terms of mathematical engagement. I used color theory and the mathematical field of optics to form my photographs, and angle tools to draw right-angle axes. It really speaks to how much

math goes into simple aesthetic creations, and asks rather than “What is influenced by math?”, “What isn’t?”.

If I were to do this project again, I think I would either choose the forest or another more picturesque backdrop than a street corner, just to spice up the photos and make them feel like they carry more weight. I like that I stuck with the straight-on angle for all five of them, because it makes most of the lines that run through the photo appear perfectly horizontal or vertical. This maximizes the appearance of a 2-D plain, and pushes the idea that you’re looking at a flat graph rather than a piece of art with visual depth. I also thought originally about being more artistic with Carmen’s outfits, but I didn’t want to distract from her body shape and the surrounding elements that made up the axes, so I think the simple outfit was okay. One thing that would’ve been cool would be if she had worn clothes that had a grid pattern on them, to further push the graph idea.


Ad Infinitum, Jonathan Ely

Ad Infinitum

The Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 …




Long ago.

Cars racing by.

It’s six in the morning.

“There goes Fred. He’s an elementary school teacher.” 

As a former teacher herself, my grandmother had quite a fondness for them.

To me, the people streaking by on the Michigan highway were more exciting –firefighters and astronauts. Maybe there was a nurse.

If we had seen her that morning, she would have been driving east, making the long, winding trip towards Marquette Hospital. It’s a two-hour drive, though. She probably lived closer to the medical center.

I never did know her name. She came and left quickly, bustling off to another calamity. An unknown variable, she shall live forever undefined to me. This is a conundrum for the defined world. We who scoff at Socrates’ musing that a wise man knows he knows nothing. The foolish Greek never encountered big data.

Roommates of mine may follow in this tradition. They are certain of their beliefs, certain of the misery of the world and are worse for it in the end. They didn’t see the cars go by that day; they didn’t eagerly munch on grapes from a Tupperware container that helped win the cold war; and they weren’t there that night. They did not rush into the hallway, hurling glances around wildly, unable to form words. And in their frenzy, they saw no savior, briskly walking towards them, scrubs swishing.

The other day, with sleep alluding me, I took a walk late at night, just after three. I came to a park bordered by a stream called Dixon Creek. The music in my earbuds was paused as I watched that bubbling torrent for a while. It was constructed of turbulent order, always there and yet never there again. But, as scientists may study their whole lives and find no answers in turbulence, I moved on, finding a large grey cat whose back I scratched. It must have been past the feline’s bedtime. Finally, I came across two wheels, the first of which was a prayer wheel like those found in Nepal. It was erected by a neighbor to commemorate a dead friend. The whole neighborhood had written prayers, placed in the wheel to be released when spun. I spun it. Why anger a ghost?

The second wheel belonged to a rusty old wheelbarrow with a “FREE” sign taped on. My grandmother used to tell me, “always be kind to everyone, you never know their burdens.” As I had spun the last wheel for someone whose stream had bubbled to a halt and likely did not necessarily need any prayers at the moment, thank you very much, I decided to spin the wheel of the wheelbarrow too, just in case it held prayers for some other poor fellow struggling with his own burden. Perhaps prayers from that second wheel flew straight up and east, crossing the Rocky Mountains and Mississippi River, before resting with an unknown nurse in northern Michigan. I’ve crossed the Mississippi many times by plane and car. One time, I crossed in a dust colored suburban. My grandfather drove; my grandmother sat with my sister and me in the back. We were following the car containing my parents as we travelled from Connecticut to our new life in Oregon. I was just three, but I remember the lummi sticks provided by my grandmother. Long and hard, the sticks made an impressive sound when struck together, perfect to accompany the exciting rhythms of Leroy Anderson that blared from the speakers. We also looked at the cars that we saw from our windows, much like that morning by the highway, inventing stories for everyone that streamed by.

Asked later, my grandfather said it was “the best wedding anniversary we’ve ever had.” Given the racket that we were making behind him, I am tempted to think that he was lying, but since he is the most honest man I have ever known, I must then conclude that he is, instead, slightly mad. Kant was equally mad when he turned to monstrous buildings and ferocious storms to discuss the sublime. The silly man needed only to walk up to a stranger and ask, “who are you?” It is there that we can find infinity. The enormous complexity of the human mind and spirit is enough to leave you standing in awe. All humans have lives, as infinitely complex as your own, and feelings, opinions, fears, burdens, all infinite. But it gets worse!  They just keep living every day, increasing the infinity bit by bit. Then go to an intersection, or crowded café. You will watch as infinitely complex people rush by you, like a raging flood where our own infinity is but a trickle. In this vast torrent of humanity, my grandmother’s current is almost done bubbling. When I was a senior in high school, she suffered a stroke, leaving her with extremely limited mental capability. My mother and I flew to upper Michigan in March to aid as we could. With my uncle and grandfather, we took turns sitting with her at night, making sure that in her confusion she wouldn’t wander or injure herself further. It was one night that she would not listen to me, when she insisted on getting up, that I darted into the hallway with terror in my eyes. I could not form complete sentences as I pleaded for help, but she came anyway. She talked with my grandmother patiently, helping her back to bed. She wasn’t our normal nurse who would come regularly to check in. Instead, she was a stranger who I never saw again, and I love her. I wish that I could describe all the infinities of this stranger’s life, where she grew up, if she has children, if she likes pineapple on pizza. But like a car on the highway she burst into my life, providing aid and respite, before rushing off towards the horizon. 

I wish too that I could tell you everything about my grandmother. How she was one of the first female instructors at Michigan Technological University, how she stood up to a crooked cop who abused two youthful vagabonds, or how, as a member of the league of women voters, she followed the all-male city council to a bar in order to prove that they were making deals behind closed doors and off the public record. But I cannot, just as I cannot stop the flood of time or save her from a brain’s collapse. So, I will instead leave you with a thought as your own story infinitely unfolds. You may call it the Norma Lee Stuart Conjecture if you wish. Take note of the nameless who stream around you, you know not their burdens…

Ad Infinitum 

Ad Infinitum, Author’s Description

There’s a word that I quite like, sonder. Its not a word that can be found in Webster’s dictionary, it hasn’t quite hit the mainstream. It was created in a project called the “Dictionary of Obscure Sorrows,” which aimed to put words to feelings that had been previously undefined. The following definition is given: sonder is “the realization that each random passerby is living a life as vivid and complex as your own.” When I came upon this phrase I was immediately reminded of my grandmother and our early mornings making up stories for the people that drove by on the road below us. Since she became injured, I have thought about that memory a lot. I believe that my grandmother was the first person to instill the feeling of sonder within me. It has also occurred to me that few people will ever know her incredible story, unless I told them. Unfortunately, I knew that no short story could ever contain such a meaningful life, so I instead aimed to create a broader, more applicable narrative. 

I hoped to capture the infinity of humanity in my story. By following the form of the Fibonacci Sequence, I attempted to visually capture the unfolding process that occurs when you get to know someone. Each line could be thought of as a day, the words contained then become the lived experiences of the individual which expand into infinity. Ideally, if I have done my job right, this will instill in you a feeling of sonder. I hope too that it will encourage you to call your grandmother if you can.