Model of the Real Part of the Function Cos Z by Richard P. Baker, Baker #444
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.
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 = a + bi, where i represents the square root of negative one and a and b are real numbers. 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 – this model), and #446 (MA.211257.094). The models came to the Smithsonian in 1956 after exhibition at MIT.
label: Description
content: Just as complex numbers have real and imaginary parts, so do functions of them. This model represents the real part of the function cos (Z). If, as before, Z = a + bi, it represents the values of the product cos a cosh b, where cosh b is the hyperbolic cosine of b.
label: Description
content: The model has a wooden base and sides, with a white plaster surface representing values of cos (Z). A tag on the side reads: No. 444 (/) The real part of Cos Z.
label: Description
content: Values of the cosine, which run from -1 to +1 and back to -1, form the upper edge of the two higher opposite wooden sides. The upper edge of the other two opposite sides are values of -cosh b, with values of this function running from -1 to 0 to -1 (-coshb is the value of the function cos a coshb whien cosa = -1, as it does in the planes that contains these sides). Values of the product of the two functions within these intervals are represented by the plaster surface.
label: Description
content: Baker also designed a model for the imaginary part of the function cos (Z), but it does not survive in the collections.
label: Description
content: Reference:
label: Description
content: Richard P. Baker, Mathematical Models, Iowa City, 1931, p.17.
label: Description
content: Accession file 211257.
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.211257.093
label: accession number
content: 211257
label: catalog number
content: 211257.093
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 screwed to base (overall production method/technique)
label: Measurements
content: average spatial: 15.9 cm x 16 cm x 17.1 cm; 6 1/4 in x 6 5/16 in x 6 23/32 in