Model for the Horopter, a Space Curve of Order Three, by M. Schilling; No. 157, Ser. 28 No. 6

Model for the Horopter, a Space Curve of Order Three, by M. Schilling; No. 157, Ser. 28 No. 6

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This is one of six models designed by Walter Ludwig of Breslau on the suggestion of Felix Klein and with the participation of Frederick Schilling. It illustrates the theory of cubic space curves as applied to physiological optics. The series first appeared in 1902.
The metal model fits on a square wooden stand. It consists of a metal rod, a metal radius, a brass curve and a V-shaped copper-colored piece that moves along the curve. There are no marks on the object itself. A paper tag on the base reads: Horopter (/) 28 Serie, No. 6 (/) Verlag v. Martin Schilling, Halle a. S.
According to the web site cited below, the horopter is a space curve of order three with equations:
y = a
z = xy
In optics, it can be interpreted as the set of points for which the light falls on corresponding areas in the two retinas. It is a cubic ellipse on a cylinder with the same asymptote.
Martin Schilling, Catalog, 1911, pp. 72-74, 133.
The website showing the model collection of the University of Groningen at, accessed November 6, 2017.
Currently not on view
Object Name
Geometric Model
geometric model
date made
place made
Germany: Saxony-Anhalt, Halle
Physical Description
metal (overall material)
wood (overall material)
overall: 46.7 cm x 20 cm x 23.3 cm; 18 3/8 in x 7 7/8 in x 9 3/16 in
ID Number
catalog number
accession number
Credit Line
Gift of Brown University Department of Mathematics
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
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