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Mathematical Treasure: Bettini’s Mathematical Apiary

Frank J. Swetz (The Pennsylvania State University)

Mario Bettini (1582-1657) was a respected Jesuit scholar: a philosopher, mathematician, and astronomer. In his 1642 Apiaria universae philosophiae mathematicae, he examined various mathematical phenomena. The frontispiece shows a garden of mathematics: the author seems to be associating mathematics with the world of nature and especially bees.

The “Geometry of bees” is found on page 6 where the geometric construction of the cells within a beehive is examined and commented upon.

Geometric proportion and symmetry is recognized in the construction of a spider’s web and the converging perspective of two rows of trees.

On page 9, a demonstration of the linkage-construction of a conchoid is given. This curve is credited to Nicomedes (ca. 200 BCE), who devised it to assist in the attempts to trisect an angle and to duplicate a cube.

An hyperbola is examined as a conic section.

A solar eclipse is explained.

Information is provided on the taking of “heavenly sightings.”

The images above are supplied through the courtesy of the Peabody Library, John Hopkins University.

Index to Mathematical Treasure

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Bettini’s Mathematical Apiary," Convergence (June 2017)