Model of the Differential Geometry of a Helix by Richard P. Baker, Baker #89 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.

The typed part of a paper label on the top of the wooden base of this model reads: No. 89 (/) Diff. Geometry of a helix. The model illustrates several terms used to describe curves in three-dimensional space, using as an example the spiral curve on a cylinder known as a helix. In the model, the cylinder is represented by blue threads and the helix by a wire that twists along it. The point of interest, hereafter called P, is at the center, atop a wire extending perpendicularly from the base (the normal to the helix at the point). Shown with red threads is the osculating (kissing) plane to the helix at P. The red thread that passes through P represents the tangent line at P. The wire circular arc passing through P in the osculating plane represents part of what is called the osculating circle. The smaller circles joined by wires that pass through P form what is called the osculating cone.

Shown with yellow threads is a plane perpendicular to the osculating plane known as the normal plane. The thread on this plane that passes through P is called the binormal to the curve at P.

The model sold for $7.50.

References:

R. P. Baker, A List of Mathematical Models, [1905], p. 16.

R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 12.

R. P. Baker Papers, University of Iowa, Iowa City, Iowa.

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