Model of a Surface Associated with Archytas Made by Richard P. Baker, Baker #485
date: label: date made
content: ca 1920-1930
name: label: maker
content: Baker, Richard P.
notes: label: Description
content: In the fifth century B.C.E., Archytas, a friend of the philosopher Plato and a leader in the city of Tarentum (then a Greek territory, now in southern Italy), took an interest in such subjects as mathematics, astronomy, and music. One problem he addressed was that of finding the ratio of two lengths that would be the cube root of a given ratio of lengths. This would allow one to find, for example, a cube with twice the volume of a given cube.
label: Description
content: To solve this problem, Archytas devised a construction that combined three surfaces of revolution – a cone, a half-cylinder, and a half-torus with an inner diameter of zero. These three surfaces appear on this plaster model, with the cylinder rising vertically, the axis of the cone passing across the model, and the half-torus centered in the middle of the base. The distance between the vertex of the cone and the point where the cone, cylinder, and torus meet is the cube root of the chord where the cone cuts the base of the cylinder.
label: Description
content: A tag on the model reads: No. 285 (/) Archytas (/) The tore cylinder and (/) cone for a cube root.
label: Description
content: Heath gives a modern version of Archytas’ proof. See also MA.211257.097.
label: Description
content: References:
label: Description
content: R. P. Baker, <I>Mathematical Models</I>, Iowa City, Iowa, 1931, p. 4.
label: Description
content: Thomas Heath, <I>A History of Greek Mathematics</I>, vol. 1, Oxford: Clarendon Press, 1921, pp. 213-216.
label: Description
content: Mathematical Models at the University of Arizona, accessed June 26, 2017.
label: Location
content: Currently not on view
topic: label: Subject
content: Mathematics
setName: label: See more items in
content: Medicine and Science: Mathematics
label: See more items in
content: Science & Mathematics
creditLine: label: Credit Line
content: Gift of Frances E. Baker
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: MA.211257.096
label: accession number
content: 211257
label: catalog number
content: 211257.096
objectType: label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: plaster (overall material)
label: Physical Description
content: wood (overall material)
label: Physical Description
content: metal (overall material)
label: Physical Description
content: white (overall color)
label: Physical Description
content: copper (overall color)
label: Physical Description
content: brown (overall color)
label: Physical Description
content: black (overall color)
label: Physical Description
content: cast plaster. sides screwed. (overall production method/technique)
label: Measurements
content: average spatial: 10 cm x 14.8 cm x 14.6 cm; 3 15/16 in x 5 13/16 in x 5 3/4 in