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Various Methods to Construct a Cardioid

Various Methods to Construct a Cardioid
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2019-10-07 02:07
CircleTransformationGeometric Construction
This example demonstrates various methods to construct a cardioid, a special curve resembling a heart. Using geometric concepts such as rotation, tangent, and angle, we can construct a cardioid. The example uses GeoGebra commands like Intersect, CurveCartesian, Segment, Sequence, Circle, Tangent, Angle, Rotate, etc., suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. CurveCartesian((R / 3 * cos(t)), (R / 3 * sin(t)), t, 0, (2 * pi)) → c
  3. CurveCartesian(X(t), Y(t), t, 0, (2 * pi)) → a
  4. CurveCartesian((R * cos(t)), (R * sin(t)), t, 0, (2 * pi)) → b
  5. Segment(B, C) → f
  6. CurveCartesian((((2 * R)) / 3 * cos(t)), (((2 * R)) / 3 * sin(t)), t, 0, (2 * pi)) → d
  7. Sequence(b(((2 * pi) * t / N)), t, 0, N - 1) → l1
  8. Sequence(c(((2 * pi) * t / N)), t, 0, N - 1) → l2
  9. Circle(c(T), a(pi)) → k
  10. Segment(c(T), A) → j
  11. Circle(d(T), R / 3) → e
  12. CurveCartesian(R / 3 + (((2 * R)) / 3 * cos(t)), (((2 * R)) / 3 * sin(t)), t, 0, (2 * pi)) → m
  13. Segment(I, J) → n
  14. Tangent(J, m) → p
  15. Segment(H, G) → h
  16. Angle(J, G, A) → angle2
  17. Angle(O, H, G) → angle1
  18. Segment(G, J) → i
  19. Angle((1, 0), O, D) → angle3
  20. Angle(J, D, A) → angle4
  21. Segment(D, A) → g
  22. Segment(O, D) → l
  23. Segment(D, J) → r
  24. Corner(1, 5) → Dims1
  25. Segment(H, A) → q
  26. Rotate(D, pi / 2, A) → B2_{image}
  27. Corner(2, 5) → Dims2
  28. PolyLine((xminideal, yminideal), (xmaxideal, yminideal), (xmaxideal, ymaxideal), (xminideal, ymaxideal), (xminideal, yminideal)) → Window