Model for the Vector Product, Distributive Law by Richard P. Baker, Baker #155
date: label: date made
content: ca 1906-1935
name: label: maker
content: Baker, Richard P.
notes: label: Description
content: This geometric model was constructed by Richard P. Baker in the early twentieth century when he was Associate Professor of Mathematics at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over 100 of his models are in the museum collections.
label: Description
content: The typed part of a paper label on the edge of the wooded base reads: “No. 155 (/) Vector product; distr.law.” The number 55 is written twice on the base as are three equations, [(A+B)]C=OD”, [AC]=OA”, and [BC]=OB”. In these equations Baker is representing the vectors on the left hand side by a single upper case letter that represents the vector emanating from the point labeled O and ending at the point labeled by that letter. On the right-hand side of these equations Baker represents that same type of vector but shows the O explicitly. It should be noted that since the single upper case letters are vectors, the product means the cross product.
label: Description
content: Vectors A, B, and A+B, all lie on the base. Vector C is the vertical metal arrow and, therefore, is perpendicular to A, B, and A+B, which is the diagonal of parallelogram OADB, i.e. the vector D. Because the cross product of two vectors is perpendicular to both vectors, the cross products (A+B)C=DC, AC, and BC, are all perpendicular to C so also lie on the wooden base.
label: Description
content: The model illustrates a special case of the distributive law for the cross product of vectors, i.e., when the vectors that form the sum (here A and B) define a plane that is perpendicular to the vector being distributed over the sum (here C). In this case the parallelograms OADB and OA”D”B” are similar where A”, B” and D” are defined in the original equations. Finally, if we let U denote the unit vector in the same direction as C then [(A+B)]U=D’, [AU]=A’, and [BU]=B’ and OADB and OA’D’B’ are congruent.
label: Description
content: While there are also vertical wire pieces marking the points A, B, and D, it is not clear how the height of these wire pieces relate to the vectors.
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.211257.032
label: accession number
content: 211257
label: catalog number
content: 211257.032
objectType: label: Object Name
content: geometric model
physicalDescription: 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: red (overall color)
label: Physical Description
content: black (overall color)
label: Physical Description
content: soldered and bolted (overall production method/technique)
label: Measurements
content: average spatial: 12.2 cm x 20.3 cm x 25 cm; 4 13/16 in x 8 in x 9 27/32 in