untitled, Emily Colson

My project aims to construct what my peers find to be  the most aesthetically ideal face compiled from a pre-selected group of facial features and characteristics. In order to conduct this project I had to assemble a survey for my peers, gather the results, and implement them into the project.

With my project I have had to take some concepts that would be best suited to a larger study and cater them to the size of our class. Facial features are generally difficult to confine to defining categories, so instead of asking which type of nose (for example) my classmates found most aesthetically pleasing, I provided examples. I tried to make the examples as varied as possible. I also took my examples from people who are generally predetermined to have more aesthetically pleasing features: actresses and models. This choice was also made in order to ensure an easier completion of the project on my part, as with celebrities I can find many photos of them with different angles of the facial feature so that it is easier to understand and draw it. I decided that all the features should come from the same gender for a more coherent facial structure. If I were to have included a mix of genders I would have had to determine what gender the final grouping of features would have, and I did not feel comfortable determining that based purely off appearances.

As for gathering the data, I found all the images I would use as examples of each facial feature and compiled them into an accessible multiple choice survey which was then sent out to my peers. This way, the results could be relayed to me in a statistical format, from which I could gather which facial features were most commonly agreed upon as the most aesthetically pleasing. I decided to choose the mode to determine which features I would use, as that represented the largest consensus by my peers. 

The results of my survey are as follows: 

  • The preferred nose was option B, Zazie Beetz’s, with a majority of 56.3%
  • The preferred eyes were option C, Janelle Monae’s, with a majority of 31.3%
  • The preferred mouth was option C, Naomi Scott’s, with a majority of 56.3%
  • The preferred face shape was oval, with a majority of 37.5%
  • The preferred hair texture was wavy, with a majority of 62.5%
  • The preferred hair length was medium, with a majority of 62.5%

If I were to conduct this survey again, I would primarily look for a larger sample size. I got sixteen responses on this survey, which is almost the entire class, but is still not nearly enough to eliminate bias. Another thing I would likely change would be the selection of the examples of facial features for this project. The best way to do this would be to show only the features intended for use so the participants would not let their personal beliefs about the celebrity influence their decision. It would also be better if the examples did not come from celebrities, but I chose to do this to make the execution of the project easier, as stated above. Since I did choose celebrities, my own bias is incredibly present in this project. I chose celebrities that I could think of and also like. Thus, this project would more accurately represent which of Emily Colson’s preferred celebrities’ facial features does this class prefer. Overall, though, I believe I did the best I could with the constraints that I had.

As for the execution of the project itself, I only had a few difficulties. I love to draw, and I especially love to draw people, so this project seemed the logical choice to play into what I enjoy. I originally planned to draw this project digitally, but as I went through the process of it I was unsure of the results. I tried both traditional and digital drawings and ended up sticking with the digital because the tools allowed for a more symmetrical face.

In conclusion, this project has been a great test of both my mathematical and drawing skills. It was invigorating to create a survey and compile data; it is incredibly rewarding to see results. It was also a nice change of pace to draw for my homework instead of typical homework tasks. Overall I am happy with the results of this project.


Exploring Physics in Music, Aazaad Burn


There are many ways of making sound on an instrument, which we take for granted, and seldom precisely understand why each different technique yields a different sound.  In my creative project, I attempt to explain the physics behind the techniques that yield different sounds on the violin through a composition. The composition showcases different methods of making unique sounds on the violin using techniques such as col legno, pizzicato, natural harmonics, sul tasto, and chords.  I also included a few measures designed for the musical saw because of the interesting properties of its sound.

Project Description

The first step in my project was to make a list of the elements that make violin music aesthetically appealing, allowing me to pick the ones on which to focus.  The elements were timing/time signature, tempo, dynamics, key, timbre, and technique/effects.  I decided to choose technique/effects as my focal point because they are used much less frequently than the other five elements, and hence are often overlooked. The techniques I integrated into my piece are col legno, pizzicato, sul tasto and harmonics.  I also decided to include a few measures to be played on the musical saw because of its particularly interesting sound. 

The intersection of mathematics with these effects isn’t obvious.  However, these effects are made using physics, which is a branch of study that is closely involved with mathematics.  Violin music is created by vibrating a string, which creates standing waves, and by manipulating the waves in different ways, different effects are created.  

To play the violin in the most traditional way, a bow is drawn across a string.  The bow creates sound in the same way that plucking a string repeatedly creates a sound.  Drawing a bow across a string creates a slip-stick cycle where the bow grips the string and then releases it.  Rosin is generally applied to the bow hair to increase its coefficient of static friction.  Bowing the string too slowly makes it so you can hear the sticks exclusively and bowing too fast makes it so you can hear the slips exclusively.  When bowing a string, the entire range of high, low, and the fundamental harmonic are maintained and only dissipate when the bow stroke ends. There must be an equation or slip-stick frequency in relation to bow speed, though I do not know if it is linear, exponential, logarithmic… and I have not succeeded in finding it.  It can be determined that “the cycle of stick and slip on the bow has the same period as the vibration of the string” (Wolfe).  In my project, we will work out an equation to describe the time of a slip-stick cycle, and one for the amplitude of the motion of the string at the bowing point based on variables such as string length, distance from the bridge, and period of the vibration of the string.  

Having thus laid the foundation for understanding the physics behind bowing the violin in the traditional way, we transition to a discussion of the effects mentioned above.  

Sul Tasto refers to the technique in which the bow is drawn over the fingerboard to create a finer, more muffled sound.  The sound here is more muffled because the area where the string is vibrating most is positioned away from the f-holes.  The string vibrates most where the bow interfaces with the string, so positioning it away from the f-holes gives the impression of a muffled sound.  

The pizzicato technique yields a short burst of sound that dissipates quickly, in contrast with the long, sustained sound that a bow drawn across the string produces.  This is because drawing a bow across the string sustains the vibration without letting it dissipate, whereas a pizzicato only vibrates the string for an instant.  When a bow is drawn across a string, a note is maintained.  However, after a pluck, the high harmonics fade away quickly, leaving only the fundamental and some weak lower harmonics. Bowing maintains the rich harmonic spectrum.

Col Legno refers to tapping the string with the back of the bow that produces an effect similar to pizzicato, where we perceive a short burst of sound that dissipates quickly.  The sound dissipates quickly because striking the wood is not a continuous input of energy.  This sound has a different quality than pizzicato; it sounds drier and more staccato.  This is because we hear the collision of the stick and the string, which is percussive.

The word “harmonics” denotes the overtones that are present in addition to the fundamental frequency.  The standing wave pattern of a fundamental frequency contains only two nodes.  As we add nodes, we get to the second harmonic, then the third, etc..  When we know the number of waves in a string, we can derive an equation relating the wavelength of the standing wave to the string length.  On the violin, we can play a “true harmonic” without its fundamental frequency by placing a finger lightly onto a string in specific places, and drawing the bow across the string as usual.  To play an “artificial harmonic”, one simply places a finger as if to play a regular note, and places an additional finger lightly on the string four whole steps away.

Our final “effect” isn’t really an effect; it is a peculiar sound made by a peculiar instrument.  A sound by a musical saw is clearer than on most instruments because a saw usually only creates one single harmonic along with the fundamental frequency, instead of a broad range of harmonics, which is the reason why the sound carries so well on the wind and sounds much more clear. A sound is made when the bow is drawn across the saw which is curved into the S shape; this can also occur when the saw is in a C shape.  The player must find the “sweet spot” of the saw in order to make a sustained pitch.  The “sweet spot” is a flat part of the metal, and it can be moved up and down based on the curvature of the saw.  When the player drags the bow across the saw, they cause the saw to vibrate, which creates the sound.  Like bowing a violin, a slip-stick motion occurs here as well.  

This paper has attempted to explore some of the physics behind violin effects.  I wonder if this exploration will change the way I perceive my own playing, and I ask if my playing will be improved with this new knowledge.  I am curious if violin students would benefit from the knowledge of this physics and if it would improve their playing.  I wonder if I could put together a booklet on this. But that is a project for another time!

Works Consulted

Cox, Trevor. “Musical Saws and Harmonics.” The Sound Blog, 31 Dec. 2009,

McNamee, David. “Hey, What’s That Sound: Musical Saw.” The Guardian, Guardian News and Media, 7 June 2010,

“Physics Tutorial: Fundamental Frequency and Harmonics.” The Physics Classroom, 2000,,frequency%20of%20the%20first%20harmonic.

“Tonal Effects.” Strings – Orchestration Skills-Step 8,

Wolfe, Joe. “Bows and Strings.” The Bowed String, The University of New South Wales,


Umbilical Torus, Gavin Barrett, 2020

Overview of Project

With this piece, I set out to create an umbilical torus through the carving of a block of wood. While I recognized that this would be a very difficult endeavor, I found that after breaking the process down into more basic steps, it came together quite nicely. This leap into complex geometry lead me to encounter a variety of issues, including an utter failure of my differential geometry skills that resulted in having to restart entirely; however, after overcoming some of the obstacles, I was very happy with the piece I created and learned a great deal about woodworking, art, and geometry in the process.


In this piece, a variety of mathematics are at play, both in the final product and the creation of said product. The name of this shape is an umbilical torus, and it has become a relatively popular tangible example of calculus over the years, whether on the covers of calculus textbooks or as a statue (a rather famous one is located at Stony Brook University). The simple explanation of this piece is that it is a single edged three-dimensional shape, something which at first thought might sound impossible. Naturally, to go along with this lone edge that wraps around the body of the figure three times uniquely (and infinitely over the same track) there is only a single side to this figure as well. These traits make it a particular fascination in the field of singularity theory.

The mathematics that apply to this rather complex shape are equally complex if not more. While I can take no credit for the personal discovery of such things, the math behind the figure is as follows:

x = sin u (7 + cos(u/3 – 2v) + 2cos(u/3 + v)

y = cos u (7 + cos(u/3 – 2v) + 2cos(u/3 + v)

z = sin(u/3-2v) + 2sin(u/3-v)

for the interval:

-3.14 < u < 3.14

-3.14 < v < 3.14

These mathematics work together to form what is (in layman’s terms) a quadrilateral traveling through a three-dimensional space while orbiting a point while rotating at 90° for every orbit, meaning that each edge of the quadrilateral lines up perfectly with its adjacent side’s path following a full orbit around the center point.

As for the mathematics of creating it, there were many complications that ought to be noted. First, a proficiency in the way that the shape operates was fundamental to planning this project as it is a remarkably difficult shape to imagine when drawn two-dimensionally. However, after viewing enough angles, I felt I had a good grip on the process I would need to take (it should be noted that this shape was extremely difficult to orient without the back side). I had to take measurements of the wood block I used in order to ensure that the thickness of the “band” I was creating would be circular and devoid of serious irregularities, and then I simply had to begin carving until I had created a donut shaped piece. Following this, I had to find the circumference of the circle orbiting the center point and find the arc length of one fourth of it. Knowing that this arc length would constitute one orbit around the center point, I had figure out how much the rotation would be at smaller intervals, for example, how much rotation would occur in 1/12 of an orbit around the center point. Once I had this figured out, I connected the lines and continued this process three times around the circle until I had come back to my beginning point. After this, I grinded, whittled, carved, and sanded off the wood until the lines I had created represented the edge.

This shape has gained popularity due to its bizarre characteristics, but also its aesthetic draw, as it leads the viewer to engage in the mathematics of it as well. Upon my first viewing, I pondered whether it was even possible to create such a figure in a three-dimensional form, or whether it was simply an illusion. However, as this piece, and hundreds of other recreations of this geometric marvel have shown, it is possible, fascinating, and a remarkable example of the interaction between mathematics and aesthetics.

Last Thoughts

It is deeply unfortunate that we find ourselves in a set of circumstances wherein the three-dimensionality of this shape is lost. One of the most interesting aspects of this shape is tracing the side around the object, and simply viewing it from a variety of different angles. This being said, I hope that the curiosity of this shape is not lost in the finitude of a photograph, and I hope you can enjoy it visually and mathematically as much as I do.


untitled, Olivia Banks, 2020

My creative project is a somewhat abstract exploration of how the idea of ​recursion​ can be explored through an artistic lens.

-Elizabeth Banks

What is recursion in a mathematical sense?

According to the Cambridge Dictionary, recursion is “the practice of describing numbers, expressions, etc. in terms of the numbers, expressions, etc. that come before them in a series.” In other words, it is when something is defined by itself. This is quite broad, and recursion has many diverse applications in the field of mathematics and computer science. For example, one of the most familiar applications of recursion is the Fibonacci sequence: ​F​(​n)​ = ​F(​ ​n​ − 1) + ​F​(​n​ − 2). The reason it is recursive is because it uses numbers within its own set to define subsequent numbers within the set.

How does recursion present itself in the artistic world?

While recursion can seem quite complex mathematically, it actually presents itself quite simply in an artistic sense. One somewhat famous example of recursion in art is called the Droste effect. It originated from this packaging design:

In the image on the package, there is an image of the same package.

The Droste effect can be seen widely throughout the artistic world in the form of images containing their own image. 

How can I apply recursion to my own art-making?

While the Droste effect is an easily recognizable and succinct application of the idea of recursion, I really wanted to push myself further into how I could represent this idea in my own way. As an artist, I am always drawn to self-portraiture, especially in oils. I thought it would be fun to do my creative project in my own artistic style, as if it could simply be part of my existing portfolio. With this in mind, I chose my subject and my medium: a self-portrait in oils.

In order to really manipulate the idea of recursion into a more abstract representation, I chose to do my portrait on a mirror. This represents recursion because, when I look at my self-portrait, me, the subject, stares back in the mirror. In this way, it is almost like an image is depicted with an image; the viewer defines the content of the piece. While this is not the most straightforward way to present recursion in art, I thought it best suited my artistic style, and it was a unique and abstract way to present a mathematical topic.


Clark Honors College, Faculty in Residence application

When I was last on the academic job market in 2008, I was torn between positions at liberal arts colleges and research universities. I had offers from excellent liberal arts schools, including Claremont McKenna College and Bucknell College, but ultimately decided to come to UO so that I had an opportunity to supervise graduate students. I enjoy supervising undergraduate students as well, and have advised four CHC Honors theses, three departmental Honors theses, and several other undergraduate research/reading projects. Supervising students is my favorite aspect of the job. Beyond the usual reward one finds in sharing knowledge with others, getting to know our varied students—understanding their knowledge and skills, their likes and dislikes, and their dreams for the future—is the major driving force keeping me in academia.

I am applying for a Clark Honors College, Faculty in Residence position so that I can pursue the academic work I love in an environment where it is rewarded.

My research lies at the intersection of number theory, probability and mathematical statistical physics. This is a fascinating genre of mathematics research, with many opportunities for undergraduate research. The connection with physics allows intuition to be brought to bear on mathematical problems, which in turn allows undergraduates to make meaningful contributions to mathematical research—at least in the form of conjectures, and discovery of new phenomena.

I also enjoy reading mathematics broadly, and have experience supervising students on mathematics research that is either outside my educational background or applied to other domains of knowledge.

Besides supervision of research, I am also interested in undergraduate mathematics education, especially for students who may not ultimately pursue a degree in a quantitative/scientific field. Mathematics is simultaneously the language of the universe and a ubiquitous tool in modern life. Mathematics education tends to favor the latter, but it is in the former where the rich beauty of mathematics lies. The aesthetics of mathematics is often invisible to individuals who view it only as a tool. I would like to bring this aesthetic vision of mathematics to undergraduates (and others) who may not otherwise experience the sublime beauty of mathematics.

An example of a seminar I would like to offer would be the Development of New Numbers. Such a seminar could trace the history and necessity of new kinds of numbers (natural, integer, rational, algebraic, transcendental, real, complex, etc) as human knowledge has developed. I see such a seminar lying at the intersection of history, philosophy and mathematics, and I would interweave group exercises/projects to motivate the mathematics and inform the necessity (and beauty) of the development of new numbers.

Besides teaching, supervision and research, I also engage heavily in university service. Currently I am the Past President of the University Senate and the President of United Academics, as well as a member of many other committees (including chair of the Core Ed Council). I see some of my current service as fulfillment of certain projects/initiatives started as Senate President. My experience working on core education may be useful in any curricular redesign happening in CHC. While I expect to always be involved in university service, I also expect the level to subside from the current high-water mark. I enjoy the challenge of leadership, but I also wistfully dream of a time when I can fill my days reading, doing math, working with students and doing a sensible amount of service, and hopefully earning the rank of full professor.

Finally, I would like to underscore my commitment to the diversification of mathematics (and science more broadly). Much of this problem arises from enculturation of expectations by society at large, but many issues arise from an old guard of mathematicians who propagate racial and gender disparity via preferential treatment for men and microaggression towards others. These attitudes are incongruent with how I view myself as an educator and scholar, and I look forward to working in a unit that values the various backgrounds and experiences of our students, faculty and staff.


BA/BS Modeling

Each circle represents a 4-credit course to be distributed among the categories of Language, Quantitative Literacy, Writing & Cultures, and the Areas of Inquiry: Natural Sciences, Social Sciences and Arts & Letters and Other. You may edit the names of the categories. Currently the Bachelor of Arts requires 12 credits more than the Bachelor of Sciences—these are represented by the lighter colored circles.

Bachelors of (specify)

Natural Sciences
Social Sciences
Arts & Letters
Quantitative Literacy
Writing & Cultures
Writing 121
Writing 122/123
Other (specify)

Post your proposed degree.

Drag the circles to the categories and create your own Bachelors degree. Click on “Post your proposed degree” to send your proposed degree to the comments. This will result in some HTML code appearing in the comments text area below. Just hit “Post Comment” and your proposal will appear in the comments!

You may edit the text within each circle, for instance to designate a specific course. This has been done with Writing 121, 122/3 and a course in U.S. Cultures: Difference, Inequality, Agency (DIA) and one in Global Perspectives (GP). These courses are currently considered immutable because their requirements are recently specified by Senate legislation. We have categorized these writing courses and US:DIA, GP under the heading Writing & Cultures to unify and simplify the presentation of requirements to students.

Things to think about when dragging and editing:

  • The total number of credits should be the same between the BA and BS
  • Based on the Rule of Thirds for undergraduate degrees: 1/3 credits for Core Ed, 1/3 for the major and 1/3 for exploration, and the 180 credit requirement for Bachelors degrees, solutions which use fewer of the light gray circles are preferable.
  • Currently courses are allowed to double-dip betwixt Areas of Inquiry and between an Area of Inquiry and US:DIA or GP. Thus it may be possible to satisfy requirements without taking a course for each circle appearing in the diagram.
  • Currently courses which satisfy the BA or BS may not be used simultaneously to satisfy an Area, US:DIA, or GP requirement. We should discuss whether it is preferable, feasible and/or necessary to relax this prohibition.
  • The current requirements for Areas of Inquiry are actually 15 credits per Area—not four courses per Area. This is to ease transferability, and the vast majority of our students meet this requirement by taking four courses.
  • We are rethinking our BA/BS requirements; do not feel constrained by our current requirements when distributing courses.
  • If you have creative ideas about how BA or BS specific courses, sequences or programs should work, please email me.

Current Category Descriptions

Continue reading “BA/BS Modeling”

These Fonts Here

Google Fonts integration with WordPress (and a convenient Gutenberg block) has changed web design for the better. You can now easily choose from 700+ free fonts to type-up your webpage.

Check out a few of my favorites and why I chose them for this site.

Cormorant Garamond

If it were up to me, I’d always write in a font like Garamond (or the pretty well-done bastardization offered here). But it’s not a good font for the web. It’s not chunky enough for good legibility; even on paper it can be a tad effete. So I kept looking for the basic content font for this site.

Avería Serif Libre

Now here’s a web font! Avería Serif Libre is chunky enough to be legible on a screen. It’s serifed, but barely, and it has a slightly blurry appearance that lends personality. The reason for this is amazing—it’s formed by averaging all the serif fonts in Google’s font collection! You can read all about it here. As a probabilist, how could I resist?

Avería Serif Libre is the basic content font for this site.

Open Sans CONDENSED 700

I loves me some condensed sans serifs. Open Sans Condensed (here in the 300 weight) is the font for all subheadings (in ALL CAPS). The Open Sans collection is an excellent sans font that goes well with everything. The condensed version is tight, but legible, and the 700 weight makes a good heading font.

Archivo NARROW

The default heading font for the theme (Ixion) is Archivo Narrow in ALL CAPS. It still appears in menus, buttons and featured content because I haven’t gotten around to changing the CSS. It’s a good font, especially if you’re stuck with it.

Faster One

I chose this one for the header, because it looks FAST! Also, when I’m in a hurry I sign my email -=C