Painting - Mystic Hexagon (Pascal)

Description:

This painting is based on a theorem generalized by the French mathematician Blaise Pascal in 1640, when he was sixteen years old. When the opposite sides of a irregular hexagon inscribed in a circle are extended, they meet in three points. Pappus, writing in the 4th century AD, had shown in his Mathematical Collections that these three points lie on the same line. In the painting, the circle and cream-colored hexagon are at the center, with the sectors associated with different pairs of lines shown in green, blue and gray. The three points of intersection are along the top; the line that would join them is not shown. Pascal generalized the theorem to include hexagons inscribed in any conic section, not just a circle. Hence the figure came to be known as "Pascal’s hexagon" or, to use Pascal’s terminology, the "mystic hexagon." Pascal’s work in this area is known primarily from notes on his manuscripts taken by the German mathematician Gottfried Leibniz after his death.

There is a discussion of Pascal’s hexagon in an article by Morris Kline on projective geometry published in James R. Newman's World of Mathematics (1956). A figure shown on page 629 of this work may have been the basis of Crockett Johnson's painting, although it is not annotated in his copy of the book.

The oil or acrylic painting on masonite is signed on the bottom right: CJ65. It is marked on the back: Crockett Johnson (/) "Mystic" Hexagon (/) (Pascal). It is #10 in the series.

References: Carl Boyer and Uta Merzbach, A History of Mathematics (1991), pp. 359–62.

Florian Cajori, A History of Elementary Mathematics (1897), 255–56.

Morris Bishop, Pascal: The Life of a Genius (1964), pp. 11, 81–7.

Date Made: 1965

Referenced: Pascal, BlaisePainter: Johnson, Crockett

Location: Currently not on view

See more items in: Medicine and Science: Mathematics, Science & Mathematics, Crockett Johnson, Art

Exhibition:

Exhibition Location:

Credit Line: Ruth Krauss in memory of Crockett Johnson

Data Source: National Museum of American History

Id Number: 1979.1093.05Catalog Number: 1979.1093.05Accession Number: 1979.1093

Object Name: painting

Physical Description: masonite (substrate material)wood (frame material)metal (frame material)Measurements: average spatial: 124.5 cm x 63.5 cm; 49 in x 25 in

Guid: http://n2t.net/ark:/65665/ng49ca746a9-6543-704b-e053-15f76fa0b4fa

Record Id: nmah_1098877

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