Olivier Models at Columbia University

 

Attention is called to the photographs of string models. The models are by Olivier of Paris, and are part of a collection in the possession of the Department of Engineering Drafting of Columbia University.

 

So ends the Preface of Charles H. Schumann's Descriptive Geometry. A Treatise on the Graphics of Space for the Scientific Professions (Fourth edition, 1946; the first was 1927). This statement along with some of the figures in the book confirm that Columbia University once owned several Olivier models. It is not known if these models survive at Columbia.

When models were ordered for USMA in 1857 Charles Davies got the catalog from his son-in-law, Peck at Columbia.

Peggy Kidwell mentions that there are such models at Columbia in "American mathematics viewed objectively - the case of geometric models, pp. 197-208 in Vita Mathematica: Historical research and Integration with Teaching, edited by Ronald Calinger, Washington, D.C., Mathematical Association of America, 1996. She gives no reference.

 

Fig. 186, p. 244. String Model of a Left-hand Helical Convolute. A Single Curved Surface Formed by Tangents to a Helix.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This surface is developable "since a tangent intersects the helix in two points, the second of which is contained in the next position of the tangent. Two consecutive tangents intersect and therefore lie in a plane."  This concept of curve is interesting, for it agrees with that of L'Hospital in the first calculus book, Analyse des Infiniment Petits, 1696, §3.

 

Figs. 193 and 194, p. 266. String Models of Hyperbolic Paraboloid, showing double ruling. Two straight line directrices and a plane directer.

Although not specifically identified as an Olivier model, this is quite similar to the Union College model, Union-5.

 

Fig 196, p. 269. String Model of a Right Conoid. One straight line, one semi-circular directirx and a plane directer perpendicular to the straight line.

 

This is quite similar to Union-19, except that this model does not illustrate the movement that the line has in the Union model. Bell-3 is somewhat different in that the frame that holds the semi-circular directrix is not planar but cylindrical.

 

Fig 199, p. 272. String Model of an Oblique Cylindroid. A circular directrix with its diameter equal to the minor axis of an elliptic directrix and a plane directer through the major axes of the ellipse at oblique angle.

 

Similar to Bell-1.

 

Fig. 201, p. 273. String Model of a Skew Arch (Cylindroid). Two semi-circular directrices in non-parallel plandes and a horizontal plane directer.

 

 

 

Fig. 202, p. 274. String Models of Hyperbolid of Revolution of One Nappe, showing double ruling of reversing the straight-line generatrix.