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Hooked on Conics

Where geometry and art meet

David Schoonmaker

About seven weeks before each issue’s deadline, the American Scientist staff gathers for what we call an issue-planning meeting. In truth, by that point the editors have decided the contents of the upcoming issue and who will be responsible for what. So it’s really a meeting to describe each column and article to the assembly—to murmurs (we hope) of approval. Often the theme of this essay becomes apparent at that meeting.

The June 19 rendition of this six-times-a-year ritual turned up cones. First off was the description of Henry Petroski’s Engineering column, “A Portrait of the Artist as a Young Engineer” (pages 368–373). Actually, it’s not primarily about cones—it looks deeply into the engineering education of sculptor Alexander Calder—but they do figure in a section of the piece. Henry describes the difficulties budding engineers face in visualizing and drawing how planes intersect cones. In particular, he describes the travails of imagining what will happen when a hexagonal pencil is worked in a conical pencil sharpener, noting that this is frequently drawn incorrectly. This mention got the full attention of the associate art director, a Pratt Institute graduate with extensive background in mechanical drawing. In preparing the figure you see on page 371, Tom confirmed that “about half the time” illustrators get it wrong.

About then, our managing editor piped up with a summary of the feature article by Daniel S. Silver, “Slicing a Cone for Art and Science” (pages 408–415). Albrecht Dürer didn’t think of himself as a mathematician. Instead, he viewed mathematics—and geometry in particular—as a tool to assist in accurately depicting the beauty of the world. In the Painter’s Manual he described, among other things, the many shapes formed when planes intersect cones—including parabolas, hyperbolas and, significantly, ellipses. At risk of spoiling the story, I’ll just say that the correspondence of astronomer Johannes Kepler specifically mentions Dürer.

A close runner-up for the issue’s theme goes to comparatively simple elements turning out to be bit more complex than anticipated. What could be simpler than hydrogen? Its molecular form, H2, was an early candidate for study by this issue’s Marginalist, Roald Hoffmann. He made some with his hobby chemistry set as a youth, revisited it in high school with similar incendiary results and, to his great surprise, returned to dihydrogen much later in his career as a theoretical chemist. In “Bonding to H2” (pages 374–378), he describes some mighty peculiar behavior attributable to this fundamental molecule.

Later on Keith A. Jenkins reveals some surprising traits exhibited by a one-atom-thick layer of carbon—graphene. In “Graphene in High-Frequency Electronics” (pages 388–397), he tells us why this material, first extracted only eight years ago, could be the basis for some higher-speed circuitry, as semiconductors near their limits of scalability.

Finally, be sure to review this issue’s Classic, “The Big Picture” (pages 382–387), wherein we review some of the magazine’s finest illustrations over the years. I may be stretching it a bit to liken this to entries on the periodic table, but it certainly contains the visual rendition of Strunk and White’s elements of style.—David Schoonmaker

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