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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
Dr. Chr. Wiener
Karlsruhe in 1884
Mark 60 (for eight pieces)
Schilling, M., Catalog mathematischer Modelle für den höheren mathematischen Unterricht, Leipzig: Verlag von Martin Schilling, 1911