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?