Drawing Some Plane Curves Using Envelopes of Lines

​
curve
parabola
​
An alternative to drawing a curve by plotting points is to draw it as the envelope of its tangent lines. Some of the envelopes in this Demonstration have applications in string art.

Details

This was a project for Advanced Topics in Mathematics II, fall 2016, Torrey Pines High School, San Diego, CA.

References

[1] T. Iwamoto. "Lines and Circles." (Feb 1, 2017) www.takayaiwamoto.com/Lines_Circles/Lines_Circles.html#hypocycloid.
[2] A. Rossiter. "String Art." (Feb 1, 2017) www.antiprism.com/album/865_string _art/index.html.

External Links

Epicycloids from an Envelope of Lines
Generating a Cardioid VII: Joining Points on a Circle
Catacaustics for Some Graphs
Catacaustics Generated by a Point Source

Permanent Citation

Carine You
​
​"Drawing Some Plane Curves Using Envelopes of Lines"​
​http://demonstrations.wolfram.com/DrawingSomePlaneCurvesUsingEnvelopesOfLines/​
​Wolfram Demonstrations Project​
​Published: February 3, 2017