Model of the Absolute Value of Cos Z by Richard P. Baker, Baker #446
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. Plaster on top, it has wooden sides and base, both painted black. The plaster is color-coded, with a scale on one side explaining the meaning of the spectrum of colors used. A paper tag taped to one side reads: No. 446 The absolute value (/) of Cos Z.
label: Description
content: Particularly from the nineteenth century, mathematicians and physicists have found it useful to consider functions of complex numbers, that is to say numbers of the form Z = x + yi, where i represents the square root of negative one and x and y are real numbers. Just as complex numbers have real and imaginary parts, so do functions of them. This model represents the absolute value of the function cos (Z) where, as before, Z = x + yi. This consists of positive values of the equation (cos <sup>2</sup>x cosh<sup>2</sup> y + sin<sup>2</sup>x sinh<sup>2</sup>y) <sup>1/2</sup>. This equation can be reduced to (cos<sup>2</sup>x + sinh<sup>2</sup>y)<sup>1/2</sup>. In the model, values of the angle x run from 0 to 2 pi , while those of y run from roughly -3 to 0 to roughly +3. The colored scale indicates regions corresponding to different values of x. For smaller and for larger values of y, values of sinh<sup>2</sup>y become much larger and the small fluctuations associated with the first term in the equation would not be visible.
label: Description
content: Baker’s 1931 catalog listed seven models which he grouped as relating to the field of complex analysis; examples of four of these survive at the National Museum of American History. These are his #443 (MA.211257.092), #310 (MA.211257.050), #444 (MA.211257.093), and #446 (MA.211257.094 – this model). The models came to the Smithsonian in 1956 after exhibition at MIT.
label: Description
content: References:
label: Description
content: Baker, R.P., <I>Mathematical Models</I>, Iowa City, 1931, p.17.
label: Description
content: Accession file 211257
label: Description
content: http://math.pugetsound.edu/~martinj/courses/spring2010/m352/ComplexVariables_Sec33.pdf , accessed August 27, 2020.
label: Description
content: https://functions.wolfram.com/ElementaryFunctions/Cos/visualizations/5/, accessed August 27, 2020.
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.211257.094
label: accession number
content: 211257
label: catalog number
content: 211257.094
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: red (overall color)
label: Physical Description
content: yellow (overall color)
label: Physical Description
content: orange (overall color)
label: Physical Description
content: green (overall color)
label: Physical Description
content: plaster cast.panels screwed. (overall production method/technique)
label: Measurements
content: average spatial: 8.2 cm x 16.5 cm x 15.7 cm; 3 7/32 in x 6 1/2 in x 6 3/16 in