Painting - <I>Mystic Hexagon (Pascal)</I>
date: label: date made
content: 1965
name: label: referenced
content: Pascal, Blaise
label: painter
content: Johnson, Crockett
notes: label: Description
content: 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 <I>Mathematical Collections</I> 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.
label: Description
content: There is a discussion of Pascal’s hexagon in an article by Morris Kline on projective geometry published in James R. Newman's <I>World of Mathematics</I> (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.
label: Description
content: 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.
label: Description
content: References: Carl Boyer and Uta Merzbach, <I>A History of Mathematics</I> (1991), pp. 359–62.
label: Description
content: Florian Cajori, <I>A History of Elementary Mathematics</I> (1897), 255–56.
label: Description
content: Morris Bishop, <I>Pascal: The Life of a Genius</I> (1964), pp. 11, 81–7.
label: Location
content: Currently not on view
setName: label: See more items in
content: Medicine and Science: Mathematics
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content: Science & Mathematics
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content: Crockett Johnson
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content: Art
creditLine: label: Credit Line
content: Ruth Krauss in memory of Crockett Johnson
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: 1979.1093.05
label: catalog number
content: 1979.1093.05
label: accession number
content: 1979.1093
objectType: label: Object Name
content: painting
physicalDescription: label: Physical Description
content: masonite (substrate material)
label: Physical Description
content: wood (frame material)
label: Physical Description
content: metal (frame material)
label: Measurements
content: average spatial: 124.5 cm x 63.5 cm; 49 in x 25 in