Week 10 Reflections

Hawksley, A. J. (2015, July). Exploring ratios and sequences with mathematically layered beverages. In Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (pp. 519-524).

Summary

The research elaborates on how this workshop utilizes the flexible ingredient ratios in beverages to explore and teach fractions and integer sequences. Various ratios of sugar to water result in different densities, allowing for layering. Moreover, this characteristic enables visually compelling effects when food coloring is added to the layered drinks.

The workshop conference is divided into three sections, designed to support educators interested in developing activities. The first section focuses on discussing ratios and fractions. The second section delves further into integer sequences. The final section addresses the abstract and pedagogical aspects of the workshop, including guidance on creating layered beverages.

Initially, the beverage is layered according to a monotonic integer ratio. For instance, the bottom layer may contain 5 teaspoons of simple syrup per unit volume, while the top layer contains 3 teaspoons of simple syrup per unit volume. In this case, the sweetness ratio is 3:5 (3/5). Of course, the participants can test their calculations by creating layers and comparing their sweetness. They can also try layering the two layers. If they are incorrect about which layer is denser, then the layers will mix when they pour the less sweet layer first. 

Furthermore, this experiment can be applied to different mathematical realms. For example, participants can explore triangular numbers, Lucas numbers, and the Fibonacci sequence. They can make lemonade and may find that the intensity of flavors increases exponentially as they go down the layers. If the proportion of sugar for layer Fn can be represented per unit volume, and the proportion of lemon juice is Fn-1, we find that the ratio of sugar to lemon juice approximates the golden ratio. This approximation becomes more accurate the further down the drink you go.

People often overlook the fact that cooking is inherently mathematical. The concept of ratios and proportions in the cooking process involves some fundamental mathematics that may surprise you and prompt you to consider underlying mathematical theories.

Stops

“Everybody loves food, which makes it a perfect vehicle for conveying mathematical ideas to the general public.” (p. 1)

This quote reminds me of the affinity and acceptability inherent in food. Whether I have learned about how artists transcend national boundaries and resolve conflicts through the communal experience of food, or I have utilized food as a motivator to integrate interdisciplinary approaches in my past teaching experiences, I have come to realize that food not only fulfills a fundamental physical need but also serves as a catalyst for fostering peace and happiness.

“While this workshop describes an exercise intended to be fun and educational for all ages, it is also possible to make adult layered drinks where the density of the layers is adjusted by the fraction of alcohol in the drink.” (p. 5)

When I read the sentence from the quote, I couldn't help but laugh because it's such a charming idea. It reminds me that exploring life around us isn't just about education; it's also about satisfying our own curiosity. Perhaps we don't always need to ponder the purpose of life or search for deep meaning or take things too seriously. The essence of experiencing life is simply to enjoy it, and value will naturally emerge from that enjoyment.

Question

Have you ever explored mathematics by foods? If there is a chance, what food do you want to try?