Perimeter Testing 1: Parallelogram Perimeter and Random Experiments

Perimeter Testing 1: Parallelogram Perimeter and Random Experiments
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2016-09-30 19:51
①This GeoGebra example dynamically demonstrates perimeter measurement of a parallelogram combined with random experiments, visually showing how perimeter relates to side lengths and diagonals. ②Core mathematical concepts include properties of parallelograms, perimeter calculation, random experiments (possibly Monte Carlo methods), and indefinite integrals as a background notion. ③Construction highlights: using Point, Segment, and Line commands to create points (A, B, C, D, etc.) and segments (f, g, h, etc.), constructing a parallelogram via parallel lines, and incorporating random points for perimeter testing. ④Suitable for middle school geometry to explore perimeter variations, or for introductory probability experiments, and as a dynamic geometry demonstration for beginners.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 4]) → B
  2. Segment(A, B) → f
  3. Point(Circle[A_1, 4]) → B_1
  4. Segment(A_1, B_1) → f_1
  5. Point(Circle[A_2, 4]) → B_2
  6. Segment(A_2, B_2) → f_2
  7. Point(Circle[A_3, 4]) → B_3
  8. Segment(A_3, B_3) → f_3
  9. Point(Circle[A_5, 4]) → B_5
  10. Segment(A_5, B_5) → f_5
  11. Point(Circle[A_6, 4]) → B_6
  12. Segment(A_6, B_6) → f_6
  13. Point(Circle[A_7, 4]) → B_7
  14. Segment(A_7, B_7) → f_7
  15. Point(Circle[A_{14}, 4]) → B_{14}
  16. Segment(A_{14}, B_{14}) → f_{14}
  17. Point(Circle[A_4, 4]) → B_4
  18. Segment(A_4, B_4) → f_4
  19. Point(yAxis) → C
  20. Line(C, D) → g
  21. Point(Circle[A_8, 4]) → B_8
  22. Segment(A_8, B_8) → f_8
  23. Line(E, F) → h