Mathematical Selfies with an Artist’s Perspective - By Kathy Jaqua

Mathematical selfies can be a great way to see what someone knows or doesn’t know about a particular topic, as we have talked about in earlier posts, and glean some information about common understandings and misunderstandings.  Selfies also offer an opportunity to see the photographer’s passion while revealing the mathematical world of the individual.  One of my students in a liberal studies mathematics class is an artist with a passion for photography.  Her excitement about completing a project to explore mathematics through photography was evident by the gleam in her eye and the far away look that followed my description of the assignment.   I’d like to share some of her work as a way to take a quick look at one student’s combination of a personal passion with a personal view of mathematics. 

As Jess moved around campus with her camera--a quick snapshot with a phone was not sufficient for her passion--she looked for geometric shapes as one category of the assignment.  Her work, however, was much more than simple photos of common shapes.  Using her artist’s eye for perspective, she was able to effectively translate between 2D and 3D to capture images of geometric objects.  Here’s some of what she saw.

Rectangular Perspective

Across the highway from our campus is a beautiful conference center that Jess visited in her mathematical selfies walk around campus.  She began her trip to NCCAT through the tunnel that connects the two campuses.  This is a place that students have decorated with a variety of comments, slogans, and other messages.  From the title of her photo, the artist saw those messages as descriptive of the object itself, but it also reveals her view of how a 2D rectangle can be seen within a 3D object in the world.  She saw a rectangle in the light at the end of the tunnel. Her ability to combine what she knows is the shape of the other end of the tunnel with a sense of perspective allows her to turn an explosion of light into a clearly articulated rectangle complete with a description that captures the essence of the definition using a combination of formal and informal language.

Trapezoidal Shape

Continuing on through the grounds of NCCAT, Jess encountered a gate on the path to the pond that lies in front of the conference center.  Before passing through the arch, she stopped to note the geometric form at the top of the passage.  This time, her definition is formal and taken from an external source, but she does demonstrate her understanding of this definition with the figure in red that she added to the photo.  I found it particularly interesting that while she had no trouble seeing the shape and photographing it, she was not comfortable describing this shape in the informal manner that she used to describe the more common rectangle.  Her ability to see a trapezoid among all the shapes that are part of the arch reveals her ability to focus on some parts of a structure, and it also reveals her appreciation of symmetry.

A Cone in the Water

Passing through the archway, Jess shows us another part of an artist’s understanding of perspective with her photo of an overflow drain.  Rather than choosing to photograph the large jet of water rising from the center of the pond, Jess found a quieter shape that shows a cone as part of its construction.  This time, her sense of 3D perspective is obvious in the red figure traced on the top of the drain.  In her definition, again a combination of formal and informal language, Jess notes the 3D nature of the cone and describes how that definition translates into this object.  Like the 2D rectangle, this 3D shape does not push her to find an external source for a definition.  Does this indicate that a trapezoid is less commonly recognized in our world?

Mathematical selfies of geometric shapes are some of the easiest for students to capture.  In the case of a student who is drawn to visual representations and photography in particular, those selfies can illustrate a much deeper sense of the geometric structure of our world.  Not only are these photographs beautiful, they illustrate her sense of perspective that seamlessly combines 2D and 3D objects.

Pride of the Mountains Marching Band Selfies -- By Axelle Faughn

Western Carolina University is famous for the quality of its band. The fact that a mathematically inclined mind is more often than not also musically inclined, means that several of our students in the mathematics department do play an instrument in band. With intensive band practice almost every day of the week, we were bound to see some creative submissions from this aspect of their lives.

Band Placement on a Grid

Imagine yourself as a freshman, first day on campus a week before regular students arrive; indeed, band practice requires you to get acquainted with campus life before classes start. Next thing you know the band director instructs you to get into formation and be ready to follow instruction: the photograph on the right is what you must picture in your head. Of course, the grid helps you position yourself, and the numbers help understand the symmetry of the band structure. Although not a traditional cartesian coordinate plane, this is not very different from the day Descartes was lying in bed and decided to add a grid to his ceiling where a fly had just landed, so he could describe its specific position.

Octagonal Percussion

Now that you know where to stand during band practice, it is time for you and your new friends to pull out your instruments. Once again you realize mathematics is omni-present. This photograph of a drum pad nicely illustrates the need for regularity and symmetry in many musical instruments. If you pay attention you will also find this regularity and symmetry in the rhythm of the music itself.

Symmetrical Band Formation

Game day is finally here! Practice pays off as the crowd cheers you on and you aptly perform the choreography long rehearsed through a series of rotations and translations, which allows band performers to keep various symmetrical arrangements while playing. Supporters await half-time with excitement and anticipation, but of course you are ready, and you don't let them down. Well done!

String Tangency

Game is over, back to the dorm. But let us not forget your other musical friends, those whose instrument is not so conducive to band practice, but still reveals plenty of mathematical connections. This photograph of a cello with the bow positioned tangential and perpendicular to the string helps us understand the proper position for a better sound on string instruments. As a cello player myself, I can assure you that for your ear's sake, you would not want the bow to be placed any other way. The student who submitted this also noted the relationship between pitch and string width, string length, and string density, which most musicians intuitively understand, and most mathematicians can explain using derivatives.


We hope you have a chance to see our Pride of the Mountains Marching Band someday. Their performance is really worth the side trip to our small mountain town, and their fame is the reason why many prospective students choose to join the student body at Western Carolina University.