Previous
Serie V
Next

# Serie V, Nr 5c

## Four forms of the cyclide of Dupin. Spindle cyclide; one sheet of the surface lying
on another and joint by two real double points.

**Mathematical description**

The Dupin's cyclides are characterized by the property that all their lines of curvature are pieces of
circles or straight lines.
The standard examples are: the ring cyclides, the spindle cyclides and the horn cyclides.

The model shows the case of the spindle cycloid with 2 imaginary double points and 2 real double
points.
The spindle cyclide is a cyclide formed by the inversion of a spindle torus.
The spindle torus is one of the three standard tori and given by the parametric equations:
**
**

** ***x* = (c + a cos(*v*)) cos(*u*)
*y* = (c + a cos(*v*)) sin(*u*)
*z* = a sin(*v*),

**
**
with c < a.
Inversion is the process of transforming points *P* to their inverse points *P'*.
The 2 real double points connect components that are lying on each other.
**Title model and translation**

Vier Formen der Dupin'schen Cyclide. Spindelcyclide; zwei reelle Knotenpunkte vereinigen zwei
ineinander liegende Flächenmäntel.

Four forms of the cyclide of Dupin. Spindle cyclide; one sheet of the surface lying on another and
joint by two real double points.

**Text on Sticker and translation**

Dupin'sche Cyclide.

Cyclide of Dupin.

**Designer**

Dr. P. Vogel under the supervision of Dr. A. Brill

München in 1880

**Company**

Martin Schilling in Halle a.S.

**Original price**

Mark 7,50

**Dimension**

10-11 cm

**Material**

Plaster

**Literature**

Schilling, M., Catalog mathematischer Modelle für den höheren
mathematischen Unterricht, Leipzig: Verlag von Martin Schilling, 1911