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 We construct the evolute of the cardioid as the envelope of the normals to the curve.
Click the linked diagram below and then the ‘Animate’ button to generate the evolute of the cardioid. Click the button again to stop the generation. Describe the mechanics of this generation. Clicking the little x at bottom right will clear the drawing from the applet window. You can try dragging the drive point Q rapidly around the circle, but the normals quickly fill the window. Can you describe the generated figure here? What is the curve? How does it relate to the original cardioid?
The evolute of the cardioid is another cardioid with base circle having the same centre as that of the original cardioid, but one third of the radius. The orientation of the evolute is opposite to that of the original curve.
BIBLIOGRAPHY
http://mathworld.wolfram.com/CardioidEvolute.html
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