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# Reihe VII, nr 512

## Generalized helicoid (helicoid consisting of line segments of the same length) with curves on it perpendicular to all this
lines (helices).

**Mathematical description**

The model is a general helicoid which is a ruled surface.
The surface is generated by rotating a line segment around its midpoint and, at the same time,
displaced in perpendicular direction at constant velocity.
The model has two turns around the axis.
On the model you can see different helices, which are the curves on the surface with has at every point the same distance to the axis.

When you look at the model from an infinite far point you can see a family of cycloids.
When you look at all the double points (point where the curve intersect itself) generated by this family of cycloids this is a curve which is
also a cycloid.
This cycloid has half of the period as the original cycloids.
The movement of this cycloid depent on where you let the point go to infinite.
One of these cycloids which intersect the axis is also showed on the model.

**Title model and translation**

Sechs Drahtmodellle von Dreh- und Schraubenflächen. Wendelfläche (gerade geschlossene Schraubenfläche) mit
Haupttangentenkurven (Schraubenlinien).

Six wire models of rotated surfaces and helicoids. Generalized helicoid (helicoid consisting of line segments of the same length) with curves
on it perpendicular to all this lines (helices)

**Text on Sticker and translation**

Missing sticker.

**Designer**

H. Wiener

Frankfurt in 1896

**Company**

H. Wiener in Dresden

**Original price**

Mark 100

**Dimension**

36-36-80 cm

**Material**

Metal

**Literature**

Verzeignis Mathematischer modelle; H. Wieners sammlung mathematischer modelle, Verlagsbuchhandlung B.G.Teubner, Leipzig, 1905