Envelope of the sliding ladder
- Zoltán Kovács
- Parametric Curves
A ladder (shown as segment AB) is leaning against the wall and sliding down. Drag point A to slide the ladder. Try to express the contour of its trace by using an algebraic expression.
By using GeoGebra's Envelope command you can find the algebraic object. Also you can see 4 copies of the same curve, which as a whole, is called astroid. Red lines are the tangents of the astroid.
- Find the 6th order polynomial manually. Compare your result with http://en.wikipedia.org/wiki/Astroid.
- Also compare your result with http://en.wikipedia.org/wiki/Envelope_(mathematics)#Example_4.