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Intersection Area and Partial Volume in 2D by Ron van den Burg

Intersection Area and Partial Volume in 2D by Ron van den Burg
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2019-01-01 00:30
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the intersection area and partial volume in a 2D space. Key mathematical concepts include area, intersection, and volume. Using GeoGebra commands such as Segment, Intersect, and Polygon, complex geometric shapes can be constructed. Suitable for high school mathematics education, particularly in coordinate geometry and solid geometry.

GeoGebra Commands & Parameters

  1. Segment(V_{--}, V_{+-}) → E_{b}
  2. Segment(V_{+-}, V_{++}) → E_{r}
  3. Segment(V_{++}, V_{-+}) → E_t
  4. Segment(V_{-+}, V_{--}) → E_l
  5. Segment(P_1, P_0) → E_{P01}
  6. Segment(C, P) → t_{<0}
  7. Segment(C, P) → t_{>0}
  8. Angle(A, C, If[t > 0, P, (3 * C) - (2 * P)]) → α
  9. Angle(If[t > 0, P, (3 * C) - (2 * P)], C, A) → β
  10. Intersect(E_{P01}, E_{b}) → I_{b}
  11. Intersect(E_{P01}, E_{r}) → I_{r}
  12. Intersect(E_{P01}, E_t) → I_{t}
  13. Intersect(E_{P01}, E_l) → I_{l}
  14. Segment(I_{b}, I_{t}) → l
  15. Segment(I_{l}, I_{r}) → m
  16. Segment(I_{b}, I_{r}) → n
  17. Segment(I_{r}, I_{t}) → p
  18. Segment(I_{t}, I_{l}) → q
  19. Segment(I_{l}, I_{b}) → r
  20. Polygon(V_{--}, I_{b}, I_{t}, V_{-+}) → q1, v_{--}, i_{b}, i_{t}, v_{-+}
  21. Polygon(V_{--}, V_{+-}, I_{r}, I_{t}, V_{-+}) → poly2, v_1, v_{+-}, i_{r}, i_1, v_2
  22. Polygon(V_{--}, V_{+-}, I_{r}, I_{l}) → q2, v_3, v_4, i_2, i_{l}
  23. Polygon(V_{--}, V_{+-}, V_{++}, I_{t}, I_{l}) → poly1, v_5, v_6, v_{++}, i_3, i_4
  24. Polygon(I_{b}, V_{+-}, V_{++}, I_{t}) → q3, i_5, v_7, v_8, i_6
  25. Polygon(I_{b}, V_{+-}, V_{++}, V_{-+}, I_{l}) → poly3, i_7, v_9, v_{10}, v_{11}, i_8
  26. Polygon(V_{--}, I_{b}, I_{r}, V_{++}, V_{-+}) → poly4, v_{12}, i_9, i_{10}, v_{13}, v_{14}
  27. Polygon(I_{r}, V_{++}, V_{-+}, I_{l}) → q4, i_{11}, v_{15}, v_{16}, i_{12}
  28. Polygon(I_{b}, V_{+-}, I_{r}) → t1, i_{13}, i_{14}, v_{17}
  29. Polygon(I_{r}, V_{++}, I_{t}) → t2, i_{15}, i_{16}, v_{18}
  30. Polygon(I_{t}, V_{-+}, I_{l}) → t3, i_{17}, i_{18}, v_{19}
  31. Polygon(V_{--}, I_{b}, I_{l}) → t4, i_{19}, v_{20}, i_{20}
  32. Polygon(V_{--}, V_{+-}, V_{++}, V_{-+}) → q5, v_{21}, v_{22}, v_{23}, v_{24}
  33. LaTeX(Term_{t,0}, false, true) → TextTerm_{0}
  34. LaTeX(Term_{t,1}, false, true) → TextTerm_{1}
  35. LaTeX(Term_{t,2}, false, true) → TextTerm_{2}
  36. LaTeX(Term_{t,3}, false, true) → TextTerm_{3}
  37. LaTeX(Term_{t,4}, false, true) → TextTerm_{4}
  38. LaTeX(Term_{t,5}, false, true) → TextTerm_{5}
  39. Segment(P_{--}, P_{+-}) → E_{x-}
  40. Segment(P_{+-}, P_{++}) → E_{+x}
  41. Segment(P_{++}, P_{-+}) → E_{x+}
  42. Segment(P_{-+}, P_{--}) → E_{-x}
  43. Segment((φ, 0), (φ, (2 * t_{max}))) → s_φ
  44. Segment((φ, 0), Result) → s
  45. If(Defined[l], Length[l], If[Defined[m], Length[m], If[Defined[n], Length[n], If[Defined[p], Length[p], If[Defined[q], Length[q], If[Defined[r], Length[r], "Error"]]]]]) → LengthCheck