Model of a Surface Associated with Archytas Made by Richard P. Baker, Baker #485

Object Details

Baker, Richard P.

Description

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. 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.

A tag on the model reads: No. 285 (/) Archytas (/) The tore cylinder and (/) cone for a cube root.

Heath gives a modern version of Archytas’ proof. See also MA.211257.097.

References:

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.

Mathematical Models at the University of Arizona, accessed June 26, 2017.

Location

Currently not on view

Credit Line

Gift of Frances E. Baker

ca 1920-1930

ID Number

MA.211257.096

accession number

211257

catalog number

211257.096

Object Name

geometric model

Physical Description

plaster (overall material)

wood (overall material)

metal (overall material)

white (overall color)

copper (overall color)

brown (overall color)

black (overall color)

cast plaster. sides screwed. (overall production method/technique)

Measurements

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

See more items in

Medicine and Science: Mathematics

Science & Mathematics

National Museum of American History

Subject

Mathematics

Record ID

nmah_1087312

Metadata Usage (text)

CC0

GUID (Link to Original Record)

https://n2t.net/ark:/65665/ng49ca746a9-4159-704b-e053-15f76fa0b4fa