Model for a Proof Associated with Archytas by Richard P. Baker, Baker #485a

Model for a Proof Associated with Archytas by Richard P. Baker, Baker #485a

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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.
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. This wire model with a wooden base illustrates the proof underlying Archytas’ theorem.
A tag on the model reads: No. 285 s (/) Archytas. The proof. One of (/) the earliest known.
Heath gives a modern version of Archytas’ proof. See also MA.211257.096.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 4.
Thomas Heath, A History of Greek Mathematics, vol. 1, Oxford: Clarendon Press, 1921, pp. 213-216.
Currently not on view
Object Name
geometric model
date made
ca 1920-1930
Baker, Richard P.
Physical Description
wood (overall material)
metal (overall material)
paper (overall material)
soldered.stuck into holes. (overall production method/technique)
average spatial: 6.8 cm x 15.1 cm x 15 cm; 2 11/16 in x 5 15/16 in x 5 29/32 in
ID Number
accession number
catalog number
Credit Line
Gift of Frances E. Baker
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
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