Model for Elementary Analytic Geometry by Richard P. Baker, Baker #230

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.

The images of this model show portions of two curves in two dimensions with a paper label attached to one of the metal curves. The typed part of this label reads: “No. 230 (/) Cos=cos cos+cos cos+cos (/) cos” with handwritten θ, α, α’, β, β’, γ, and γ’ following the seven instances of cos. As these angles are not shown on the model as it now exists, it is likely that what is labeled as Baker’s model 230 is only part of the model that represents the equation on its label.

However, the equation as written does have a clear geometric meaning related to what are known as direction cosines of a vector, i.e., the cosines of the angles that the vector makes with the x, y, and z axes. Specifically, if the angles two vectors make with the axes are α, β, γ, and α’, β’, γ’ then the equation given as the title of this model, cos θ = cos α cos α’ + cos β cos β’ + cos γ cos γ’, says that θ is the angle between the two vectors.

Currently not on view