Ask someone to name a favorite shape, and they'll probably choose one of the usual suspects: triangle, circle, maybe a trapezoid. These run-of-the-mill forms take a back seat to more sophisticated and mind-bending structures in our cover story, in which writer Rachel Crowell asks mathematicians to describe their most adored shape. The responses are not only colorful; they also illustrate why mathematics once fell under the rubric of natural philosophy.
The drive to understand the natural world, often through abstract thinking, becomes clear in some of the essays. For instance, one mathematician says, "My favorite shape is the loop, a circle with all geometric information stripped away, leaving only a free-form one-dimensional object." Other geometric gems include a hyperbolic pair of pants, a hollow form with a waist and two ankles, and a permutahedron, "the site of a beautiful, productive dialogue among geometry, algebra and combinatorics.
" Journalist Willem Marx writes a riveting feature about the behemoth machines plunging their metallic claws into the South Pacific seafloor off Papua New Guinea (PNG) to mine metals and minerals that are critical to the economy. We the readers enter the story as Marx boards a privately owned ship, telling us he's not sure why the operators allowed a reporter to observe such a brazen project. Marx follows a slew of leads on land and at sea to find out how aware PNG regulators were of this operation, as well as to uncover the identities.
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