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Proof without words: Geometric Interpretation of Fraction Division

Proof without words: Geometric Interpretation of Fraction Division
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2020-02-27 01:34
FunctionCoordinate GeometryGeometric Construction
This example visually demonstrates the intuitive meaning of fraction division through geometric shapes. It involves key mathematical concepts such as fractions and geometric construction. Using GeoGebra commands like Vector, Polygon, and Segment, it dynamically illustrates the process of fraction division. Suitable for middle school and above students to learn the concept and geometric meaning of fraction division.

GeoGebra Commands & Parameters

  1. Vector(A, U) → v_1
  2. LCM(b, d) → o
  3. DivPoint(A, D, o) → list7
  4. DivPoint(B, C, o) → list8
  5. Polygon(A, Element[list7, t], Element[list8, t], B) → poly5, q, r, f_1, g_1
  6. Polygon(E, F, G, H) → poly2, e, f_2, g, h
  7. Segment(I, J) → i
  8. Segment(K, L) → j
  9. Textfield(a) → InputBox1
  10. Textfield(b) → InputBox2
  11. Textfield(c) → InputBox3
  12. Textfield(d) → InputBox4
  13. Polygon(A, D, C, B) → poly1, a_1, d_1, c_1, b_1
  14. DivPoint(A, D, b) → list1
  15. DivPoint(B, C, b) → list2
  16. DivPoint(E, F, d) → list3
  17. DivPoint(H, G, d) → list4
  18. Sequence(Segment[Element[list1, i], Element[list2, i]], i, 1, b) → list5
  19. Sequence(Segment[Element[list3, i], Element[list4, i]], i, 1, d) → list6
  20. Polygon(A, Element[list1, a], Element[list2, a], B) → poly3, a_2, k, l, b_2
  21. Polygon(E, Element[list3, c], Element[list4, c], H) → poly4, e_1, m, n, h_1
  22. DivPoint(E, F, o) → list9
  23. DivPoint(H, G, o) → list10
  24. Sequence(Segment[Element[list7, i], Element[list8, i]], i, 1, o) → list11
  25. Sequence(Segment[Element[list9, i], Element[list10, i]], i, 1, o) → list12
  26. Sequence(Polygon[Element[list7, (t * i)], Element[list7, (t * (i + 1))], Element[list8, (t * (i + 1))], Element[list8, (t * i)]], i, 1, p - 1) → list13
  27. Segment(M, N) → f
  28. Segment(O, P) → i_1
  29. Point(e_1) → V
  30. Vector(V, U) → u_1
  31. Translate(poly5, v_1) → poly4'
  32. Translate(poly3, v_1) → poly3'
  33. Sequence(Translate[Element[list11, i], v_1], i, 0, t) → liste1
  34. Translate(k, v_1) → k'
  35. Translate(a_2, v_1) → j_1
  36. Translate(B, v_1) → B'
  37. Translate(A, v_1) → A'
  38. Segment(B', A') → k_1
  39. Translate(l, v_1) → l'
  40. Translate(e_1, u_1) → l_1
  41. Translate(H, u_1) → H'
  42. Translate(m, u_1) → m'
  43. Translate(n, u_1) → n'
  44. Midpoint(j_1) → W
  45. Midpoint(n') → Z
  46. Midpoint(m') → A_1