Diagonal of a Rectangular Prism by Tim Brzezinski (2)

Diagonal of a Rectangular Prism by Tim Brzezinski (2)
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2021-11-20 10:36
This example demonstrates the construction of the diagonal of a rectangular prism. Key mathematical concepts include the properties of diagonals in solid geometry and the Pythagorean theorem. Using GeoGebra commands such as PointIn, Circle, Line, and Rotate, 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

Draw a rectangular prism and show its space diagonal. First, construct the three adjacent faces of the prism. Then, draw the diagonals connecting each vertex of one face to the opposite vertex of the adjacent face. Next, calculate and draw the space diagonal of the prism, labeling its length. Finally, differentiate the diagonals with different colors or styles and display the 3D effect of the prism.
The prompt above was compiled from the original drawing commands and is for reference only.