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Making a Rectangular Prism by Scaling a Cube

Making a Rectangular Prism by Scaling a Cube
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2020-10-01 10:16
Solid GeometryTransformationGeometric Construction
This example demonstrates how to create a rectangular prism by scaling a cube. Key mathematical concepts include geometric transformations and solid geometry. It uses commands such as Dilate (scaling), Polygon (polygon), Vector (vector), Sequence (sequence), and Translate (translation). Suitable for middle school and above students to learn 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, ur, vr, uc, vc2
  14. Polygon(C, D'_2, A''_1, B'_1) → poly2, vc, wc2, vl, wl
  15. Polygon(A''_1, D'_2, F''_1, E''') → poly3, wc, uc2, wr, ul2
  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, ur2, vr2, f_4
  38. Polygon(D', C, B', A'') → poly8, d_6, wl2, vl2, a_4
  39. Polygon(A'', D', F'', A''') → poly9, a''_3, d'_5, wr2, ul
  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

AI Drawing Prompt Reference

Draw a rectangular prism solid figure. Start with a cube and scale it in three different directions (length, width, and height) to expand it into a rectangular prism. Draw the six rectangular faces of the prism: front, back, left, right, top, and bottom. Mark vectors indicating three mutually perpendicular edge directions. Draw several parallel line segments along each edge of the prism to create a grid texture, enhancing the three-dimensional effect. The overall result is a hollow rectangular prism framework with grid lines.
The prompt above was compiled from the original drawing commands and is for reference only.