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.
- 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.
- 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.
- 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.
- 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.
- Baker also designed a model for the imaginary part of the function cos (Z), but it does not survive in the collections.
- Reference:
- Richard P. Baker, Mathematical Models, Iowa City, 1931, p.17.
- Accession file 211257.
- Location
- Currently not on view
- Credit Line
- Gift of Frances E. Baker
- ca 1906-1935
- ID Number
- MA.211257.093
- accession number
- 211257
- catalog number
- 211257.093
- Object Name
- geometric model
- Physical Description
- plaster (overall material)
- wood (overall material)
- metal (overall material)
- white (overall color)
- black (overall color)
- plaster cast screwed to base (overall production method/technique)
- Measurements
- 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
- See more items in
- Medicine and Science: Mathematics
- Science & Mathematics
- National Museum of American History
- Subject
- Mathematics
- Record ID
- nmah_1087263
- GUID (Link to Original Record)
- https://n2t.net/ark:/65665/ng49ca746a9-3bb0-704b-e053-15f76fa0b4fa
