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Making a Rectangular Prism by Scaling a Cube by Susan Addington

Making a Rectangular Prism by Scaling a Cube by Susan Addington
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2016-03-31 06:28
Solid GeometryTransformationGeometric Construction
This example demonstrates how to create a rectangular prism by scaling a cube in three dimensions. Key mathematical concepts include solid geometry and geometric construction. Commands used include Dilate, Polygon, Vector, Sequence, and Translate. Suitable for middle school and above students learning solid geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Dilate(E, a, A) → E'_1
  2. Dilate(F, a, D) → F'_1
  3. Dilate(G, a, C) → G'_1
  4. Dilate(A, b, D) → A'_1
  5. Dilate(E'_1, b, F'_1) → E''_1
  6. Dilate(B, b, C) → B'_1
  7. Dilate(F'_1, c, G'_1) → F''_1
  8. Dilate(D, a, B) → D'_1
  9. Dilate(E'_1, c, D'_1) → E''
  10. Dilate(E'', b, F''_1) → E'''
  11. Dilate(A'_1, c, B'_1) → A''_1
  12. Dilate(D, c, C) → D'_2
  13. Polygon(C, G'_1, F''_1, D'_2) → poly1, c_2, g', f'', d'
  14. Polygon(C, D'_2, A''_1, B'_1) → poly2, c_1, d'_1, a'', b'
  15. Polygon(A''_1, D'_2, F''_1, E''') → poly3, a''_1, d'_2, f''_1, e'''
  16. Polygon(B, A, D, C) → poly4, b_1, a_1, d_3, c_3
  17. Polygon(C, D, F, G) → poly5, c_4, d_1, f_2, g_1
  18. Polygon(D, F, E, A) → poly6, d_2, f_1, e_1, a_2
  19. Vector(C, D) → u
  20. Sequence(Segment[Translate[C, Vector[(j * u)]], Translate[G'_1, Vector[(j * u)]]], j, 1, c - 1) → list1
  21. Sequence(Segment[Translate[B'_1, Vector[(j * u)]], Translate[C, Vector[(j * u)]]], j, 1, c - 1) → list2
  22. Vector(C, G) → v
  23. Vector(C, B) → w
  24. Sequence(Segment[Translate[C, Vector[(j * v)]], Translate[D'_2, Vector[(j * v)]]], j, 1, a - 1) → list3
  25. Sequence(Segment[Translate[C, Vector[(j * w)]], Translate[D'_2, Vector[(j * w)]]], j, 1, b - 1) → list4
  26. Sequence(Segment[Translate[F''_1, Vector[(j * w)]], Translate[D'_2, Vector[(j * w)]]], j, 1, b - 1) → list5
  27. Sequence(Segment[Translate[D'_2, Vector[(j * v)]], Translate[A''_1, Vector[(j * v)]]], j, 1, a - 1) → list6
  28. Dilate(G, (a * d), C) → G'
  29. Dilate(F, (a * d), D) → F'
  30. Dilate(F', (c * f), G') → F''
  31. Dilate(D, (c * f), C) → D'
  32. Dilate(B, (b * e), C) → B'
  33. Dilate(A, (b * e), D) → A'
  34. Dilate(A', (c * f), B') → A''
  35. Vector(D', F'') → z
  36. Translate(A'', z) → A'''
  37. Polygon(D', C, G', F'') → poly7, d'_3, c_5, g'_1, f_4
  38. Polygon(D', C, B', A'') → poly8, d_6, c_6, b'_1, a_4
  39. Polygon(A'', D', F'', A''') → poly9, a''_3, d'_5, f''_3, a'''
  40. Sequence(Segment[Translate[C, Vector[((j * c) * u)]], Translate[G', Vector[((j * c) * u)]]], j, 1, f) → list7
  41. Sequence(Segment[Translate[C, Vector[((j * c) * u)]], Translate[B', Vector[((j * c) * u)]]], j, 1, f) → list8
  42. Sequence(Segment[Translate[D', Vector[((j * a) * v)]], Translate[C, Vector[((j * a) * v)]]], j, 1, d) → list9
  43. Sequence(Segment[Translate[D', Vector[((j * b) * w)]], Translate[C, Vector[((j * b) * w)]]], j, 1, e) → list10
  44. Sequence(Segment[Translate[A'', Vector[((j * a) * v)]], Translate[D', Vector[((j * a) * v)]]], j, 1, d) → list11
  45. Sequence(Segment[Translate[F'', Vector[((j * b) * w)]], Translate[D', Vector[((j * b) * w)]]], j, 1, e) → list12