Model of Poincaré's Grenzcycle by Richard P. Baker, Baker #517

Object Details

Baker, Richard P.

Description

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.”

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.

References:

See the article on limit cycles at http://www.scholarpedia.org/ , accessed August 12, 2020.

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− 𝜌²), from the discussion of the differential equation : 𝑥+𝑦𝑦′=(𝑥𝑦′−𝑦)(𝑥²+𝑦² −1).

H. Poincaré, “Sur les courbes définies par une équation différentielle,” Journal de mathématiques pures et appliquées, 1882, (III) 8, pp. 251-296, esp. p. 280.

Location

Currently not on view

Credit Line

Gift of Frances E. Baker

ca 1906-1935

ID Number

MA.211257.102

accession number

211257

catalog number

211257.102

Object Name

geometric model

Physical Description

plaster (overall material)

wood (overall material)

metal (overall material)

white (overall color)

black (overall color)

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

Measurements

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

See more items in

Medicine and Science: Mathematics

Science & Mathematics

National Museum of American History

Subject

Mathematics

Record ID

nmah_1087390

Metadata Usage (text)

CC0

GUID (Link to Original Record)

https://n2t.net/ark:/65665/ng49ca746a9-42ab-704b-e053-15f76fa0b4fa