Math Jobs: Researchers at the University of Washington, Bothell have made an important discovery in the field of mathematical tiling.

Students regularly ask: What will I do with algebra? Does calculus have any real world application at all? Who really cares about geometry? But educators know that a plethora of different math jobs exist: professors, architects, physicists and engineers are all fine examples. In today’s article, we’ll take a closer look at a breakthrough in the field of mathematical research.

“Tiling the plane” is a term in mathematics for when the same shape can be used over and over to cover an area with no gaps or overlapping edges. For example, every triangle or quadrilateral (shapes with four sides) is capable of tiling the plane. Three categories of convex hexagons also fit the mark.

The same cannot be said of ordinary pentagons with five equal sides, which aren’t able to tile the plane. In 1918, however, German mathematician Karl Reinhardt discovered five types of non-regular pentagons that can. Fourteen new types of non-regular tiling pentagons have been classified in the years since Reinhardt’s initial discovery but decades have passed since the last one was found in 1985 by Rolf Stein.

Researchers Casey Mann, Jennifer McLoud-Mann, and David Von Derau used a computer algorithm to automatically search through sets of possible outcomes. Since the number of convex pentagons is infinite, coming up with new combinations is a more difficult endeavor than it might originally seem. It took the three mathematicians two years to arrive at a new solution to the nearly century-old puzzle.

Why is a discovery like this important to other people besides mathematicians? “Many structures that we see in nature, from crystals to viruses, are comprised of building blocks that are forced by geometry and other dynamics to fit together to form the larger scale structure,” Mann explained in an interview.

The researchers are hesitant to comment on whether more tiling pentagons can be found, but state that there is no definite evidence against it. Unknown combinations of tiling the plane may still exist, awaiting discovery.

Interested in sharing more info on different math jobs with your students? Check out our article on what you can do with a math degree and help them learn about unique opportunities to pursue different math jobs!

 

Classroom Activity: Anyone can search for new ways to tile the plane; a specialized computer program is not necessary. Begin by drawing a pentagon on a piece of paper and cutting it out to use as a stencil. How difficult is it to recreate multiple of the shape so that all of its sides fit together?

Potential Math Jobs: Mathematician, Researcher, Physicist, Architect, Astronomer

Sources: NPR, The Guardian, Fast Co. Design