Limaçons as Envelopes of Circles

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

A limaçon can be defined as the envelope of the circles that pass through a fixed point P and have centers on a given circle . In this Demonstration, P is the origin. You can vary the center of the circle (shown in red) to see the envelope (shown in blue) change. Unchecking the "show limaçon" checkbox lets you picture the envelope on your own.

Contributed by: Daniel Joseph (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Snapshot 1: when P is at center of the circle , the envelope is a circle

Snapshot 2: when P is in the interior of but not at its center, the envelope is a dimpled limaçon

Snapshot 3: when P is on , the envelope is a cardioid

Snapshot 4: when P is outside of , the envelope is a limaçon with an interior loop



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send