Have you noticed how oranges are stacked at the store? Grocers know that the most attractive and stable arrangement is a pyramid. Johannes Kepler suspected this pyramid-stacking was superior, way back in the 17th century. But the German scientist also noted that he couldn’t prove it. Sadly, like Kepler, many mathematicians may never live to see the confirmation of their discoveries. Or the full impact of their insights.
In Kepler’s case, it took nearly 400 years for mathematicians to confirm his stacking theory. And their proof now has applications that extend well beyond grocery stands. For instance, this concept has helped scientists improve radio communications.
How? Scientists use the orange-stacking concept to tightly pack various messages into radio transmissions. Think of each message as an orange. The technique suggests how they can be bundled together efficiently, without overlapping. This helps maximize information flow, which has far-reaching impacts. For instance, it ensures that long-range communications — such as those done by satellites — are less noisy and garbled.
This stacking application is one measure of the reach of geometry — the mathematics of shapes.
For centuries, mathematicians have studied geometry problems — often just for what they saw as the beauty of the math. Many people may find it hard to see the appeal or everyday uses of such math. But modern geometry is full of problems both beautiful and useful. They range from visualizing an unimaginable geometric shape (that does not yet have a real-world application) to studying the shapes of viruses — which could help scientists develop new vaccines.
Shaping the unknown
Harrison Bray runs the Mason Experimental Geometry Lab at George Mason University. That’s in Fairfax, Va. One project there challenged students to imagine what a four-dimensional, or 4-D, structure might look like.
We live in a three-dimensional, or 3-D, world. That…
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