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Semicircles in Rectangle

Semicircles in Rectangle
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2017-07-12 06:42
CircleLimitTransformationGeometric Construction
This example demonstrates the geometric construction of multiple semicircles within a rectangle. Key math concepts include rectangle, translation, reflection, limits, and geometric construction. It utilizes commands like Segment, Circle, Intersect, Semicircle, CircleArc, and CurveCartesian from GeoGebra. Suitable for high school mathematics education to illustrate geometric transformations and limit concepts.

GeoGebra Commands & Parameters

  1. Segment(B, A) → f
  2. Circle(C, 6) → c
  3. Circle(E, 6) → d
  4. Intersect(c, d) → F, G, ,
  5. Segment(B, H_1) → g
  6. Segment(H_1, H) → h
  7. Segment(H, A) → i
  8. Semicircle(D, A) → e
  9. Semicircle(B, D) → k
  10. Semicircle(H, H_1) → p
  11. Semicircle(H_1, B) → q
  12. Intersect(r, f) → I, J_1
  13. CircleArc(A, H, I) → s
  14. Intersect(s, k) → J, , ,
  15. CurveCartesian(-3 + (2 * cos(t)), -2 + (2 * sin(t)), t, ((-π)) / 2, t1) → c1
  16. CurveCartesian(-3 + (2 * cos(t)), 2 + (2 * sin(t)), t, ((-π)) / 2, t2) → c2
  17. CurveCartesian(-3 + (4 * sqrt(2)) + (4 * cos(t)), (4 * sin(t)), t, π / 2, t3) → c3
  18. CurveCartesian(-3 + (2 * sqrt(2)) + ((2 * sqrt(2)) * cos(t)), 4 - ((2 * sqrt(2)) * sin(t)), t, 0, t4) → c4
  19. CurveCartesian(x(A) + (i * cos(w)), y(A) + (i * sin(w)), w, 0, t) → a