Model of the Hyperbolic Paraboloid of Normals to a Generator of a Scroll, by Richard P. Baker, Baker #151 (a Ruled Surface)

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 typed part of a paper label on the wooden base reads: No. 151 (/) Hyperbolic paraboloid of (/) normals to a generator (/) of a scroll. The model is listed with that title in an unnamed subsection of the Differential Geometry section of Baker’s 1931 catalog. A scroll is just another name for a ruled surface and each of the yellow threads is a generator of that scroll. Since there is a horizontal blue thread and pink thread that meets the vertical yellow thread, they are normal to that generator of the yellow surface. The blue threads on the tall vertical wooden pieces appear define branches of a hyperbola thus defining the blue surface as a hyperboloid. Similarly, the pink threads on the curved shorter vertical wooden pieces appear to define parabolas thus defining the pink surface as a paraboloid. Furthermore, in several of the photographs, NMAH-DOR2013-18624, NMAH-DOR2013-18623, NMAH-DOR2013-18625, and NMAH-DOR2013-18628, the yellow surface appears to meet blue surface in a parabola, while in NMAH-DOR2013-18627 and NMAH-DOR2013-18629, the yellow surface appears to meet the pink surface in one branch of a hyperbola. Thus, if all these observations are correct, the pink surface and the blue surface are both hyperbolic paraboloids.

Reference:

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

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