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Diagonal of a Rectangular Prism

Diagonal of a Rectangular Prism
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2021-11-20 10:54
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the calculation and visualization of the diagonal in a rectangular prism. It involves core math concepts like solid geometry, Pythagorean theorem, and spatial vectors. Construction highlights include using commands like Textfield, If, PointIn, Circle, Point, Line, Rotate, Segment, Intersect, Angle, Sphere, Polygon, OrthogonalLine, Translate and objects such as a, b, c, d, f, g, InputBox1, InputBox2, etc. Suitable for high school geometry teaching or math clubs.

GeoGebra Commands & Parameters

  1. Textfield(a) → InputBox1
  2. Textfield(b) → InputBox2
  3. Textfield(c) → InputBox3
  4. Textfield(d) → InputBox4
  5. Textfield(f) → InputBox5
  6. Textfield(g) → InputBox6
  7. If(Length[Mode[l1]] ≟ 0, "No digits repeat!", "Repeated digits exist.") → text4
  8. Textfield(h) → InputBox7
  9. PointIn(Plane[(0, 0, 0), (1, 0, 0), (1, 1, 0)]) → D
  10. Circle(D, (10 * a) + b, zAxis) → e
  11. Point(e) → E
  12. Line(D, E) → i
  13. Rotate(D, ((-π)) / 2, E, Plane[(0, 0, 0), (1, 0, 0), (1, 1, 0)]) → D'
  14. Line(D', E) → j
  15. Segment(D, E) → k
  16. Circle(E, d, Line[E, E + (0, 0, 1)]) → p
  17. Intersect(j, p) → F, H
  18. Segment(E, H) → l
  19. Angle(H, E, D) → α
  20. Segment(D, H) → m
  21. Line(H, H + (0, 0, 1)) → n
  22. Sphere(H, c) → o
  23. Intersect(n, o) → I, J
  24. Segment(H, J) → q
  25. Segment(J, D) → r
  26. Polygon(D, E, H) → t1, h_1, d_1, e_1
  27. Polygon(D, H, J) → t2, j_1, d_2, h_2
  28. OrthogonalLine(J, Vector[J, D], Vector[J, H]) → s
  29. Line(H, J) → t
  30. Circle(J, sqrt((100 * f) + (10 * g) + h), s) → c_1
  31. Point(c_1) → K
  32. Segment(J, K) → f_1
  33. Line(E, E + (0, 0, 1)) → g_1
  34. Sphere(E, Radius[c_1]) → u
  35. Sphere(E, c) → v
  36. Intersect(g_1, v) → L, M
  37. Line(D, d_1) → i_1
  38. Sphere(D, d) → w
  39. Intersect(i_1, w) → N, O
  40. Translate(O, Vector[E, M]) → O'
  41. Translate(D, Vector[E, M]) → D'_{1}
  42. Polygon(D, O, O', D'_{1}) → q1, d_3, o_1, o', d'_{1}
  43. Polygon(D'_{1}, M, E, D) → q2, k_1, m_1, e_2, d_4
  44. Polygon(M, J, H, E) → q3, m_2, j_2, h_3, e_3
  45. Polygon(H, J, O', O) → q4, h_4, j_3, l_1, o_2
  46. Polygon(D'_{1}, M, J, O') → q5, n_1, m_3, j_4, p_1
  47. Segment(O', D'_{1}) → q_1
  48. Segment(D'_{1}, D) → r_1
  49. Segment(D, O) → s_1
  50. Segment(O, O') → t_1
  51. Segment(E, M) → a_1
  52. Segment(M, D'_{1}) → b_1
  53. Segment(M, J) → f_2
  54. Segment(J, O') → g_2
  55. Segment(H, O) → i_2
  56. Angle(J, H, D) → β

AI Drawing Prompt Reference

Draw a rectangular prism and calculate its diagonal. First, input the length, width, and height, then create points D and E based on the input. Rotate and translate point D to generate D' and E'. Construct line segments DE, D'E', and the diagonal DH, and calculate angle α. Use points H, D, and J to create spheres and circles, generating points K, J, and M, and finally connect these points to form multiple polygons, showing the rectangular prism and its diagonal.
The prompt above was compiled from the original drawing commands and is for reference only.