Model of Poincaré's Grenzcycle by Richard P. Baker, Baker #517
date: label: date made
content: ca 1906-1935
name: label: maker
content: Baker, Richard P.
notes: label: Description
content: This model is one of several hundred designed by Richard P. Baker, a mathematics faculty member at the University of Iowa. It has a black wooden base with a plaster surface atop it. The sides of the plaster are painted black, the top is white. A typed paper tag attached to underside of the base reads: No. 517 (/) Grenzcycle. The term “Grenzcycle” translates from German into English as “limit cycle.”
label: Description
content: In an 1882 paper, the French mathematician Henri Poincaré introduced the concept of a limit cycle. According to his definition, the limit cycle is a closed curve that satisfied a differential equation which other closed curves satisfying the same equation approached asymptotically. In this model, which follows Poincaré’s example, the limit cycle is a circle, with one spiral approaching it from the outside and a second approaching it from the inside.
label: Description
content: References:
label: Description
content: See the article on limit cycles at http://www.scholarpedia.org/ , accessed August 12, 2020.
label: Description
content: Richard P. Baker, Mathematical Models, Iowa City, 1931, p. 7. This source gives the equations Baker sought to graph.as: 𝑧= 𝜃 + log𝜌 −1/2 log(1− 𝜌<sup>2</sup>), from the discussion of the differential equation : 𝑥+𝑦𝑦′=(𝑥𝑦′−𝑦)(𝑥<sup>2</sup>+𝑦<sup>2</sup> −1).
label: Description
content: H. Poincaré, “Sur les courbes définies par une équation différentielle,” <I>Journal de mathématiques pures et appliquées</I>, 1882, (III) 8, pp. 251-296, esp. p. 280.
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.211257.102
label: accession number
content: 211257
label: catalog number
content: 211257.102
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: black (overall color)
label: Physical Description
content: plaster cast. base screwed. (overall production method/technique)
label: Measurements
content: average spatial: 6.4 cm x 20.1 cm x 20.1 cm; 2 17/32 in x 7 29/32 in x 7 29/32 in