Math Digests June 2021

Is This Some Kind of Code? You Can Solve the …

The New York Times, June 25, 2021

What would a font based on Tetris look like? What about a Sudoku font, or a juggling font? Erik and Martin Demaine, a computer scientist and an artist, have designed a multitude of “algorithmic puzzle fonts,” mathematically inspired typefaces that double as puzzles. In this article, Siobhan Roberts details how the duo create their fonts, which are brought to life here in colorful images and animations. Some of the fonts, like the “Conveyer Belt Font,” even related to unsolved mathematical problems. Whether inspired by origami or checkers, the Demaines’ designs burst with playful curiosity and joyful exploration.

Classroom Activities: origami, geometry, polygons

• Read more about the fold-and-cut process that underlies the Fold & Cut font pictured at the top of the article. Have students create their names in the font with real paper to see how the process works.
• One font described in the article is made from “polyforms.” Explore Henri Picciotto’s classroom activities on polyforms, which include a set of virtual pentominoes.

—Scott Hershberger

Here’s the mathematical secret to the cheapest student loan repayment strategy

The Denver Post, June 15, 2021

Millions of Americans have student loan debt, and many owe hundreds of thousands of dollars. A recent paper by mathematicians from Dublin City University and the University of Colorado, Boulder supplies an optimal repayment strategy. The strategy, covered by Elizabeth Hernandez for The Denver Post, is designed to minimize the total cost to the borrower. To do this, the researchers had to balance the rapidly rising compound interest against the possibility of eventual loan forgiveness. Their work has profound implications: Borrowers with the highest debt could save tens of thousands of dollars using the proposed strategy. And as Colorado student loan ombudsperson Kelsey Lesco told Hernandez, “People aren’t just in debt. They’re delaying marriage. They’re not able to have kids. They’re not able to pass a credit check to get a job. It’s a huge problem.”

Classroom Activities: exponential growth, compound interest, finances

• Explore exponential growth, discussing how it relates to the problem of compound interest. If you’d like to study compound interest specifically, try these word problems.
• Have students look up tuition and financial aid information at various institutions: community colleges, public four-year universities, and private liberal arts colleges. Were students surprised by their findings? What kind of college do they think they might want to attend?
• Engage in some financial planning with this free financial literacy lesson. Include the cost of college based on students’ answers to the previous activity.

—Leila Sloman

What Data Scientists Learned by Modeling the Spread of Covid-19

Smithsonian Magazine, June 11, 2021

Math helps us predict the future. When COVID-19 began spreading uncontrollably around the world last March, US public health experts depended on complex mathematical models to create policies to stifle disease transmission. A “model,” as Smithsonian writer Elizabeth Landau explains in her article, is a predictive tool that combines measurable data with assumptions of how those data relate to each other. Remember the campaigns pleading people to help “flatten the curve”? That curve was the steep anticipated rise in COVID deaths calculated from factors like active cases, hospital capacities, and evidence-based assumptions of what worsens the spread of disease. “Models are like ‘guardrails’ to give some sense of what the future may hold,” one expert told Landau. This story follows the research journeys of disease modelers throughout the pandemic. It discusses how experts refined their models and why abundant data helped policymakers adapt on the fly.

Classroom Activities: modeling from data

• Give students hypothetical $x, y$ data, and ask them to plot the data and arrive at a conclusion. For example, suppose the $x$ values are the set of integers between 0 and 10, representing the distance in feet between an unmasked infected person and an (imaginary) virus detector; and $y$ is a hypothetical “safety score” (where 0 is the least safe and 100 is the safest), calculated from the number of viral particles detected: $[1, 3, 4, 9, 17, 25, 30, 51, 68, 78, 98]$. In this case, students could notice that plotting the data will reveal approximately quadratic growth, $y=x^2$. Discuss what this means for disease risk. They may also notice that data don’t fit mathematical functions perfectly—some $y$ values are perfect squares, while others fall below or above $x^2$.
• Discuss the concept of weighted models by listing what factors are important for disease spread (or any other problem), and assigning them weights—coefficients that denote relative importance.
• Use data from The COVID Tracking Project to practice fitting data on spreadsheets with the trendline functions on Excel or Google Sheets. (Many online resources exist to guide them in this, including this one from Saint Louis University.)

—Max Levy

Why So Many Pandemic Predictions Failed

The Atlantic, June 1, 2021

In his new book Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else, mathematician Jordan Ellenberg explores the many surprising uses of geometry. Derek Thompson interviewed Ellenberg about Shape for The Atlantic this month. The article touches on issues from pizza to COVID-19 predictions, all of which have a surprising geometric side to them.

Classroom Activities: geometry

• In the Q&A, Thompson and Ellenberg discuss geometric metaphors in nonmathematical thinking, particularly the use of phrases like “on the one hand, … on the other hand” to evoke an image of an argument’s structure.
  • Discuss other examples of geometric thinking entering a nonmathematical realm.
  • Have students read a verbal argument such as a persuasive essay and look for appeals to visual or geometric thinking.
• Practice geometric thinking with these puzzles created by Catriona Shearer.

—Leila Sloman