Math helps us make the most out of space. Sometimes that involves familiar dimensions: Geometric rules can dictate how to stack oranges in a three-dimensional box or arrange tiles on a two-dimensional plane so that as much space as possible is used up. Other times, mathematicians answer these questions in higher dimensions. This summer, mathematician Maryna Viazovska of the Swiss Federal Institute in Zurich was awarded the Fields Medal—considered by many to be math’s highest honor—for proofs of sphere packing in space of dimensions 8 and 24. The work represents an extreme twist on a 400-year-old conjecture that stacking bowling balls in a pyramid fills nearly 75% of the available space. Viazovska is only the second woman to win a Fields Medal. “I feel sad that I’m only the second woman,” Viazovska told the Times. “I hope it will change in the future.” In this article for the New York Times , Kenneth Chang describes Viazovska’s work and gives more context on her momentous award.

Classroom activities: stacking, geometry, higher dimensions

As the buzz surrounding Maryna Viazovska’s Fields Medal win demonstrated this summer, the granting of one of math’s most prestigious prizes to a woman remains, unfortunately, big news. But over a century ago, women like Sophie Bryant were already breaking barriers in mathematics: When Bryant earned her Ph.D. in 1884, no other women in the United Kingdom or Ireland had done so. In this article, Clodagh Finn sketches the accomplishments of Bryant, who tragically died in a hiking accident 100 years ago this August.

Classroom Activities: geometry, trigonometry, calculus

Packing problems seem to be a theme in math news this month. A new paper in Journal of the Royal Society Interface shows that sea urchin skeletons resemble a mathematical packing pattern called a Voronoi pattern. These patterns look like a web or mesh whose holes, or “cells”, appear somewhat irregular. But the cell shapes actually obey strict rules. Within each cell is a “seed” that governs the cell’s shape, writes Rachel Crowell for Science News . Cells must hug their seeds tightly—if you sit down anywhere on the Voronoi pattern, the closest seed should be in the same cell as you. In this article, Crowell explains the rules of the Voronoi pattern, and some of the engineering benefits this structure may offer both the sea urchin and, potentially, human technology.

Classroom Activities: geometry, Voronoi patterns

Here’s a question you might not know is contentious: how many holes are there in an ordinary drinking straw? You could say that a straw has two holes—one on each end—but you could also say that the empty space inside the straw is just one long hole. In an article for The Independent , mathematician Kit Yates examines the straw question through the lens of the mathematical field of topology. Yates compares topological shapes to objects made of dough, which can be stretched, pulled, or squished without being fundamentally changed. To topologists, a drinking glass is the same as a plate, a mug is the same as a donut , and a pair of binoculars is the same as a pair of glasses. And a straw can be compressed down into a ring—which has just one hole.

In a game show from the 1980s called Blockbusters , participants try to connect two sides of a map of tiles. Each tile on the map is an identical hexagon. Tiles on two opposing edges are blue (one team’s color), and the other opposing edges are white (for another team). When participants answer questions correctly, a tile between the edges becomes white or blue—a point for their team. The goal: connect your team’s two edges with a path of hexagons of the same color. In this article, puzzle expert Alex Bellos describes the Blockbusters game and imagines a diamond shaped map (shown below). Bellos poses a mathematical riddle. How many configurations of the map will contain a path connecting the two blue edges? The solution requires a little math, but it mostly uses a clever trick of logic.

Classroom activities: probability, logic puzzles, percolation

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