MathPlotAI Logo MathPlotAI

Making a Rectangular Prism by Scaling a Cube by Jeff Holcomb

Making a Rectangular Prism by Scaling a Cube by Jeff Holcomb
Loading the math board and drawing, please wait…
2016-11-04 08:53
Solid GeometryTransformationGeometric Construction
This example demonstrates how to create a rectangular prism by scaling a cube. Key mathematical concepts include similar triangles and solid geometry. Using GeoGebra commands such as Dilate, Polygon, and Vector, the construction of the rectangular prism is achieved. Suitable for middle school and above students to learn solid geometry and similarity 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
  46. Textfield(j) → InputBox1
  47. Textfield(k) → InputBox2

AI Drawing Prompt Reference

Draw a rectangular prism by scaling a cube. First, draw a cube, then scale the vertices of the cube to the corresponding vertices of the rectangular prism according to the given ratios. Connect these vertices to form the faces of the rectangular prism. Finally, add the edges by translating and scaling.
The prompt above was compiled from the original drawing commands and is for reference only.