Tractrix

Parametric equations

The puller moves along the x-axis and tows an object with a rope of length L. The path is a tractrix:

t > 0 is the parameter, and the puller sits at $(Lt,0)$. At every point, the tangent segment from the curve to the x-axis has length L.

Interaction

• Fixed rope length L: change the rope length. The curve scales uniformly by L, so the framed shape stays the same
• History range t: lengthen the visible window in t and show more of the tractrix
• Time speed ω: move the tracked point along the path

What to notice

• A tractrix is the path of an endpoint towed by a rope of fixed length.
• The tangent segment has constant length L. Changing L only scales the curve, and the framed picture keeps its shape.
• The upper and lower tracks are the positive and negative branches of the same equation.

Related

• Tangent approximation
• Equiangular spiral

Further reading

• Tractrix (Wikipedia)