Envelopes

Zoltán Kovács, Apr 30, 2016

A collection of demonstrations on envelopes in GeoGebra. You need at least GeoGebra 5.0.233.0 to view most of these examples. All envelopes are computed by using real-time heavy computations with Gröbner bases. This means that the objects are draggable and the envelopes are always recomputed.


  • 1. Nephroid as an envelope
  • 2. Envelope of the sliding ladder
  • 3. Cardiod as envelope
  • 4. String art envelope
  • 5. Steiner deltoid
  • 6. Limaçon trisectrix

1.

Nephroid as an envelope

Equation of the nephroid curve is a sixth order algebraic curve, however, in this example it seems like it's of 8th order because two additional components are drawn (the two parallel tangents). It is constructed by mirroring parallel rays to the edge of the circle. Finally, the Envelope command was used.
The equation is shown by using a small script size. Even worse, if you drag point B, you can see that the coefficients of the equation will increase significantly, unless B has integer coordinates.[br]This example shows however the robustness of the underlying computer algebra system, Giac.
– Zoltán Kovács

2.

–

3.

–

4.

–

5.

–

6.

–

Information