The Math Book by DK

Author:DK
Language: eng
Format: epub, pdf
Publisher: DK Publishing
Published: 2019-06-25T16:00:00+00:00

To carbon-date organic material, researchers test a sample—here from an ancient human bone—and use Euler’s number to calculate its age from the rate of radioactive decay.

The catenary

The Gateway Arch in St. Louis, Missouri is a flattened catenary arch, designed by Finnish-American architect Eero Saarinen in 1947.

Sometimes defined as the shape a hanging chain takes if it is only supported at its ends, a catenary is a curve with the formula y = 1⁄2 × (ex + e-x). Catenaries are often found in nature and in technology. For example, a square sail under pressure from the wind takes the form of a catenary. Arches in the shape of an inverted catenary are often used in architecture and construction due to their strength.

For a long time, the catenary’s shape was believed to be the same as that of a parabola. Dutch mathematician Christiaan Huygens—who coined the name catenary from the Latin catena (“chain”) in 1690—showed that, unlike a parabola, a catenary curve could not be given by a polynomial equation. Three mathematicians—Huygens, Gottfried Leibniz, and Johann Bernoulli—calculated a formula for the catenary, coming to the same conclusion. Their results were published together in 1691. In 1744, Euler described a catenoid—shaped like a waisted cylinder and produced by rotating a catenary around an axis.

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