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Diagonal of a Rectangular Prism by Tim Brzezinski

Diagonal of a Rectangular Prism by Tim Brzezinski
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2021-11-20 10:52
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the construction of the diagonal of a rectangular prism. Key mathematical concepts include the calculation of diagonals in solid geometry and the application of the Pythagorean theorem. Using GeoGebra commands such as PointIn, Circle, Line, Segment, etc., the length of the diagonal can be dynamically shown. Suitable for middle school and above students to learn solid geometry and the Pythagorean theorem.

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

Construct a 3D solid starting from a rectangular base that lies in the coordinate plane. Choose points on that base to define two opposite corners, then form the space diagonal by connecting the corresponding diagonal endpoints. Build additional lines and segments to indicate the key diagonal-related edges, including a marked angle at the relevant corner and segments linking the corner to the intermediate intersection point. Create a sphere centered at the intersection point and use its intersections with a vertical line to obtain two points, then use these points to form several quadrilateral faces around the prism so the rectangular prism with its main space diagonal is clearly represented, with the diagonal and adjacent edges visually emphasized.
The prompt above was compiled from the original drawing commands and is for reference only.