Painting - <I>Geometric Mean (Archytas)</I>
date: label: date made
content: 1968
name: label: referenced
content: Archytas
label: painter
content: Johnson, Crockett
notes: label: Description
content: This painting demonstrates a construction for finding the geometric mean of two line segments credited to the Greek mathematician Archytas (flourished 400–350 BC), an admirer of Pythagoras. Place the line segments end to end, and draw a circle with this length as diameter. Erect a perpendicular at the point where the line segments meet (d in the figure), and consider this to be the altitude of a right triangle inscribed in the semicircle. By similar triangles, the length of the perpendicular of a triangle inscribed in a semicircle is the geometric mean of the two lengths into which it divides the diameter of the circle. Hence the length of d is the mean of the segments e and f.
label: Description
content: This painting an orange-red background, and shows a triangle inscribed in an orange semicircle. The perpendicular from the right angle of the triangle divides the triangle into triangles similar to it, painted in black and white.
label: Description
content: The painting, and the attribution of the theorem to Archytas, are based on a passage from Evans G. Valens, <I>The Number of Things: Pythagoras, Geometry and Humming Strings</I> (1964), p. 118. The figure on this page of this book from Crockett Johnson's library is annotated.
label: Description
content: This oil painting on masonite is #65 in the series. It is inscribed on the back: GEOMETRIC MEAN (ARCHYTAS) (/) Crockett Johnson 1968. It has a wooden frame.
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: 1979.1093.40
label: accession number
content: 1979.1093
label: catalog number
content: 1979.1093.40
objectType: label: Object Name
content: painting
physicalDescription: label: Physical Description
content: masonite (substrate material)
label: Physical Description
content: wood (frame material)
label: Measurements
content: overall: 38.4 cm x 62 cm x 2.5 cm; 15 1/8 in x 24 7/16 in x in