Project Draft

 Human Circuits

Week 9 Reading

Article

Hawksley, A. J. (2015). Exploring ratios and sequences with mathematically layered beverages. Bridges Conference Proceedings, 519–524.

Introduction

The article Exploring Ratios and Sequences with Mathematically Layered Beverages by Andrea Hawksley describes a creative, hands‑on workshop that teaches mathematical ideas through the construction of layered drinks. By adjusting the ratios of sugar, water, and flavorings, participants can create liquids of different densities that neatly stack in a glass. This visually striking activity serves as an accessible way to introduce or reinforce concepts such as ratios and fractions, because students must calculate sweetness levels, compare densities, and test their predictions by physically pouring the layers. When calculations are incorrect, the layers mix, giving immediate and intuitive feedback.

Beyond basic ratios, the workshop extends into the exploration of integer sequences, especially those that are monotonic, since each subsequent layer must be less dense than the one below it. Participants can construct drinks reflecting arithmetic sequences, recurrence‑based sequences, or famously, the Fibonacci sequence. In the case of “Fibonacci lemonade,” the proportions of sugar and lemon juice in each layer follow adjacent Fibonacci numbers. As the layers progress, the ratio of these ingredients approaches the golden ratio, allowing students to taste a mathematical limit in action. This multisensory approach deepens the conceptual connection between numerical patterns and real‑world phenomena.

The article also gives practical instructions for building these beverages, emphasizing the importance of beginning with the densest mixture and pouring each layer slowly over ice to keep them distinct. Hawksley highlights the broader educational value of this activity, noting that many students struggle with fractions and benefit from tactile, playful learning experiences. She argues that food is an underutilized medium for mathematics education and suggests that layered beverages, snow cones, popsicles, and even salad dressings can become “mathematical foods” when ingredient ratios are intentionally designed. Overall, the workshop demonstrates how everyday experiences—like drinking lemonade—can become rich mathematical explorations.

 

Reflection

After just finishing the article, I am struck by how unexpectedly delightful the idea of Fibonacci lemonade is. I had never imagined that a mathematical sequence—something I usually encounter in diagrams, equations, or natural patterns—could be expressed through something you can actually taste. The realization that mathematics can live inside a beverage, layered through density and sweetness, feels almost like discovering a new form of art. It makes me rethink how math and creativity can intertwine in playful and surprising ways.

What stands out to me most is how this approach transforms math from something abstract into a sensory experience. Layering drinks based on ratios and sequences is not only visually appealing but also allows for immediate, hands‑on adjustments. You can change a ratio, alter a flavor, modify the density, and instantly see the result. That freedom to experiment reminds me of how artists adjust strokes on a canvas or modify tones in a piece of music. The process feels creative, intuitive, and personal—even though it is grounded in mathematical reasoning.

Reading this also challenged my previous definitions of art. I used to think of art as something you primarily see, hear, or touch. But this example shows that taste can be an artistic medium too. The idea that flavors can encode mathematical patterns expands the boundaries of what counts as artistic expression. It makes me realize that art and math share a deep connection through structure, experimentation, and the emotions they can evoke.

 

Question

How might you reimagine a familiar mathematical idea through a different sense—taste, smell, touch, or sound?

 

Week 8 Reading

 Reading

Karaali, G. (2014). Can zombies write mathematical poetry? Mathematical poetry as a model for humanistic mathematics. Journal of Mathematics and the Arts, 8(1–2), 38–45. https://doi.org/10.1080/17513472.2014.926685

 

Introduction

Gizem Karaali’s (2014) article explores the deep connections between mathematics, poetry, and human creativity, arguing that mathematical poetry can serve as an ideal ambassador for humanistic mathematics—the view that mathematics is fundamentally a human, creative activity.

Karaali begins by reflecting on her personal journey with poetry and mathematics, describing how the two domains once felt separate in her life: poetry lived in her native Turkish, whereas mathematics belonged to her English academic world. Over time, however, she recognized that both mathematics and poetry share the core human traits of cognition, consciousness, and creativity.

The article then introduces the broader concept of humanistic mathematics, which includes both teaching mathematics in a way that values students’ lived experiences and viewing mathematics itself as a cultural, emotional, and creative human endeavor. Karaali recounts the history of this movement, including the Humanistic Mathematics Network and the founding of the Journal of Humanistic Mathematics.

A significant portion of the essay focuses on mathematical poetry as a powerful bridge between the mathematical world and the emotional, artistic world. Karaali describes poetry readings at mathematics conferences, examples of poems published in the Journal of Humanistic Mathematics, and her own development as a writer of mathematical poetry

She also shows how integrating mathematical poetry into the classroom—through reading, writing, and discussion—can help students see mathematics differently. Students in her seminars enjoyed creating mathematical poems, which challenged stereotypes and encouraged them to engage playfully and creatively with mathematical ideas.

Karaali concludes that mathematical poetry can help humanize mathematics for students and the general public. Since poetry is widely recognized as a deeply human art form, pairing it with mathematics invites more people to appreciate the creativity, emotion, and humanity inherent in mathematical practice.

 

Reflection

Karaali’s article deepens our class discussion about viewing both mathematics and art as forms of creative human expression. She argues that mathematics is not just a technical subject but something rooted in the most essential aspects of being human: cognition, consciousness, and creativity. This perspective helped me rethink how mathematics can connect with poetry and other artistic practices.

One of the first places I paused while reading was the statement: “Translation from one natural language to another of mathematical texts may be deceptively simple, but note that mathematics itself is speaking a language of its own” (p. 39). This idea highlights the deep relationship between mathematics and poetry because both are forms of language that rely on structure and pattern. In this sense, they share an identity as systems for expressing meaning. Later, Karaali writes, “My mathematics and my poetry did not play together. They spoke different languages. They were of two different worlds” (p. 40). This made me think about people who are comfortable with mathematics but do not feel confident writing poetry. It raised an interesting question for me: if mathematics is already a complete language, could it be used on its own to create a meaningful poem? The possibility of writing a poem entirely in mathematical symbols feels both challenging and exciting, and it expands my understanding of what mathematical expression could look like.

Another important moment in the article appears when Karaali observes her students creating mathematical poetry: “In the classroom as they wrote and afterwards as they read their work, I could see that my students were engaged and enthusiastic about the ongoing creative process” (p. 43). This illustrates how creativity brings together the three human ingredients she emphasizes. Students enjoyed mathematics more when they could use it as a space for expression rather than as a task where correctness is the only goal. Traditional math learning often becomes exclusive because students do not experience joy until they “master” the material, and many give up before reaching that point.

Overall, the article suggests that humanistic mathematics can challenge traditional views of the subject and make it more inclusive. Through creativity—and especially through mathematical poetry—mathematics becomes a more inviting and human activity.

 

Question

What would happen to our relationship with mathematics if we all began to see it, not as a gatekeeper of correctness, but as a deeply human practice rooted in imagination, interpretation, and creativity?