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# Serie XI, Nr 8

## Over the dependence of the return elements of the projections of a space
curve on the curve itself.

**Mathematical description**

These models were made by Wiener in order to give a relation between the singularities of a space curve and
the singularities of their projections on the normal, rectifying and osculating planes.
The model shows a point *P* on the curve, the tangent line *t* at that point and the osculating plane *S*.
It also shows the projection of this space curve on the three planes.
There is a character + or - associated to each of the three elements.
*P* = + ⇔ *P* continues to move in the same direction along the curve.
*t* = + ⇔ *t* continues to rotate in the same direction.
*S* = + ⇔ *S* continues to revolve in the same direction.

This model shows the type *P*=-, *t*=-, *S*=-.
In this case *P* is a singular point.

**Title model and translation**

Acht draht-modelle; Über die abhängigkeit der Rückkehrelemente der
Projectionen einer
unebenen Curve von denen der Curve selbst.

Eight string-models; Over the dependence of the return elements of the projections of a space
curve on
the curve itself.

**Text on Sticker and translation**

missing sticker.

**Designer**

Dr. Chr. Wiener

Karlsruhe in 1884

**Company**

Martin Schilling

**Original price**

Mark 60 (for eight pieces)

**Dimension**

11-17 cm

**Material**

String

**Literature**

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