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GeoGebra Illustration: 4 Divided by 5/4

GeoGebra Illustration: 4 Divided by 5/4
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2015-01-29 01:53
VectorCoordinate GeometryGeometric Construction
This example demonstrates the geometric computation of 4 divided by 5/4, derived from the Indiana 1896 attempt to redefine Pi. It involves core math concepts like fraction operations, division, vectors, and geometric constructions. Key GeoGebra commands used include Segment, Point, Polygon, Vector, and Translate for constructing the illustration. Suitable for high school mathematics education to understand the connection between fractional division and geometric representation.

GeoGebra Commands & Parameters

  1. Segment(B1, B17) → a
  2. Segment(B1, C1) → b
  3. Segment(B2, C2) → c
  4. Segment(B3, C3) → d
  5. Segment(B4, C4) → e
  6. Segment(B5, C5) → f
  7. Segment(B6, C6) → g
  8. Segment(B7, C7) → h
  9. Segment(B8, C8) → i
  10. Segment(B9, C9) → j
  11. Segment(B10, C10) → k
  12. Segment(B11, C11) → l
  13. Segment(B12, C12) → m
  14. Segment(B13, C13) → n
  15. Segment(B14, C14) → p
  16. Segment(B15, C15) → q
  17. Segment(B16, C16) → r
  18. Segment(B17, C17) → s
  19. Segment(C1, C17) → t
  20. Point(yAxis) → A
  21. Point(yAxis) → B
  22. Segment(A, L) → a_1
  23. Segment(L, G) → b_1
  24. Segment(B, G) → c_1
  25. Segment(A, B) → d_1
  26. Segment(K, F) → e_1
  27. Segment(J, E) → f_1
  28. Segment(I, D) → g_1
  29. Segment(H, C) → h_1
  30. Polygon(L, A, B, G) → poly1, l_1, a_2, b_2, g_2
  31. Vector((1, -8), (1, -8 + o)) → u
  32. Translate(L, u) → L'
  33. Translate(A, u) → A'
  34. Translate(B, u) → B'
  35. Translate(G, u) → G'
  36. Polygon(L', A', B', G') → poly1', l', a', b', g'
  37. Vector(A, (v * x(B6), -1 + v * 2)) → w
  38. Translate(L, w) → L'_1
  39. Translate(A, w) → A'_1
  40. Translate(B, w) → B'_1
  41. Translate(G, w) → G'_1
  42. Polygon(L'_1, A'_1, B'_1, G'_1) → poly1'_1, l'_1, a'_1, b'_1, g'_1
  43. Vector(A, (z * x(B11), -1 + z * 2)) → u_1
  44. Translate(L, u_1) → L'_2
  45. Translate(A, u_1) → A'_2
  46. Translate(B, u_1) → B'_2
  47. Translate(G, u_1) → G'_2
  48. Polygon(L'_2, A'_2, B'_2, G'_2) → poly1'_2, l'_2, a'_2, b'_2, g'_2
  49. Segment(B5, C5) → i_1
  50. Segment(B9, C9) → j_1
  51. Segment(B13, C13) → k_1
  52. Segment(B16, C16) → m_1
  53. Segment(K, F) → n_1