Lines for running points

The interactive geometry tool provides a nice feature: drawing a line for a point when another point runs on a line. With that feature, you are able to construct curves like:

If one uses in addition the tool 'point on a line running with another one', one will even be able to construct:

cissoids

The cissoid in the construction below is the dotted red line. It consists of the locations of the red point, when the blue one runs around the green circle. In the MacTutor History of Mathematics archive, you can learn more about cissoids.

In the construction below, drag the the different points to see how the cissoid changes. Click the left mouse button together with the 'Control' key to get a menu. You can then make your own constructions!

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The Limacon of Pascal

The Limacon of Pascal (the dotted red line) consists of the locations of the red points in the construction below, when the blue points runs around the green circle. In the MacTutor History of Mathematics archive, you can learn more about the limacon of Pascal.

In the construction below, you can drag the points to see how the the limacon changes. Click the left mouse button together with the 'Control' key to get a menu. You can then make your own constructions!

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Lissajous Figures

Lissajous figures are the geometric locus of an intersection point, see the construction below for details. In the MacTutor History of Mathematics archive, you can read more about Lissajous Figures.

Drag the the different points to see how the lissajous figure changes. The bar on top of the construction defines the speed of the green point - this points runs 50*speed (0 <= speed <= 1) times around the circle when the blue one makes one round.

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A circle rolling on another one

The red (resp. green) figure is the locus of the red (resp. green) point, when the blue one runs around the circle. The green point is the location of a fixed point on the small circle when this circle rolls on the large one. The red point is just the green one reflected at the radius of the large circle.

Drag the the orange, blue or pink point to see how the figure changes. Note that the green and the red figures are tangent to each other in every point.

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References


© Oliver Labs, Algebraic Geometry Group, University of Mainz, Germany

Interactive Geometry Project, impressum