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The Cardioid

The Cardioid. By Stuart Blankenship & Hans Parshall. What does it mean?. Cardioid, coming from the Greek roots ‘ cardi ’ for ‘heart’ and ‘- oid ’ for ‘resembling’, roughly translates to “heart-shaped.”. Who Was Involved?. Ole Christensen Rømer 17 th century Danish astronomer

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The Cardioid

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  1. The Cardioid By Stuart Blankenship & Hans Parshall

  2. What does it mean? Cardioid, coming from the Greek roots ‘cardi’ for ‘heart’ and ‘-oid’ for ‘resembling’, roughly translates to “heart-shaped.”

  3. Who Was Involved? Ole Christensen Rømer • 17th century Danish astronomer • Made the first quantitative measurements of the speed of light • Studied the cardioid to find the best form of gear teeth

  4. A Special Case Of… The Limaçon

  5. A Special Case Of… The Epicycloid

  6. Parametric Equations The parametric equations x(t)= 2r(cost – (1/2)*cost) y(t)= 2r(cost – (1/2)*cost) create a cardioid similar to the one shown on the left. r is the radius of each of the circles.

  7. Polar Equation r(θ)= a(1-cosθ) where a is the radius of one of the two circles in the previous slide Area (3/2)*pi*a Length 8*a Other Properties

  8. Trace of an Epicycloid

  9. Trace of an Epicycloid

  10. Trace of an Epicycloid

  11. The Evolute • Cardioid • Evolute • Radius of the • Circle of Osculation

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