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Modular Section 3: Triangles

Modular Section 3: Triangles
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2020-09-11 06:29
TriangleTrigonometrySolid Geometry
This example demonstrates the modular section of a cube, focusing on the geometric properties of triangles. Key mathematical concepts include triangles, solid geometry, and trigonometry. Using GeoGebra commands such as Circle, Point, Rotate, and Cube, various faces of the cube and triangles are constructed. Suitable for middle school and above students or teachers for geometric construction and solid geometry education.

GeoGebra Commands & Parameters

  1. Circle(O, r, xOyPlane) → c
  2. Point(c) → A1
  3. Rotate(A1, π / 2, O) → A2
  4. Cube(A1, A2, zAxis) → a, A3, caraBCGF, caraCDHG, caraEFGH, aristaAD_1, aristaAB, aristaBC_1, aristaCD, aristaAE_1, aristaDH, arista, A4, aristaEF, aristaBF, aristaFG_1, aristaCG_1, aristaGH_1, A5, A6, A7, A8, caraABCD, caraADHE, caraABFE
  5. Midpoint(A1, A7) → centro
  6. Sequence(Max[0, Min[1, t - s]], s, 0, 6) → sl
  7. Midpoint(A4, A8) → B4
  8. Midpoint(A6, A2) → B2
  9. Line(A5, A3) → k
  10. Segment(A7, A1) → h
  11. Midpoint(A1, A5) → B1
  12. Midpoint(A3, A7) → B3
  13. Midpoint(A1, A2) → B5
  14. Midpoint(A2, A3) → B6
  15. Midpoint(A3, A4) → B7
  16. Midpoint(A4, A1) → B8
  17. Midpoint(A5, A6) → BA
  18. Midpoint(A6, A7) → BB
  19. Midpoint(A7, A8) → BC
  20. Midpoint(A8, A5) → BD
  21. Midpoint(A1, A6) → O1
  22. Midpoint(A2, A7) → O2
  23. Midpoint(A3, A8) → O3
  24. Midpoint(A8, A1) → O4
  25. Midpoint(A5, A7) → O5
  26. Vector(A1, A6) → u1
  27. Vector(A2, A5) → u2
  28. Vector(A3, A6) → u3
  29. Polygon(A1, A6, A7, A4) → c1, a_1, b_1, c_1, d_1
  30. Polygon(A5, A6, A3, A4) → c3, e_1, f_2, g_2, h_2
  31. Translate(c1, u1) → c1'
  32. Polygon(A8, A5, A2, A3) → c2, f, g, i, j
  33. Translate(c2, u2) → c2'
  34. Translate(c3, u3) → c3'
  35. Translate(c1', Vector[((-sl(1)) * u1)]) → c1''
  36. Translate(c2', Vector[((-sl(2)) * u2)]) → c2''
  37. Translate(c3', Vector[((-sl(3)) * u3)]) → c3''
  38. Line(B1, B2) → t_1
  39. Polygon(A1, A2, A7, A8) → c4, a1, p_2, a7, q_2
  40. Vector(A2, A7) → u4
  41. Translate(c4, u4) → c4'
  42. Translate(c4', Vector[((-sl(4)) * u4)]) → c4''
  43. Point(a7) → A
  44. Polygon(centro, A6, A7) → t1, l, a_2, c_2
  45. Polygon(centro, A1, A4) → t2, a4, m, n
  46. Polygon(A4, A8, centro) → t3, p, q, a8
  47. Polygon(A1, centro, A5) → t4, a5, s, e
  48. Polygon(A1, A5, A2) → t5, a2, f_1, g_1
  49. Polygon(A4, A8, A3) → t6, a3, h_1, i_1
  50. Polygon(A3, centro, A8) → t7, j_1, k_1, l_1
  51. Polygon(A2, centro, A5) → t8, m_1, n_1, p_1
  52. Polygon(A2, A6, centro) → t9, q_1, r_1, s_1
  53. Polygon(A3, centro, A7) → t10, i_2, j_2, d_2
  54. Polygon(A2, A3, A7, A6) → c5, k_2, l_2, m_2, b_2
  55. Polygon(A1, A2, A3, A4) → c6, n_2, r_2, s_2, t_2
  56. Translate(ll1, Vector[(sl(7) * v / 2)]) → ll2
  57. Mirror(ll2, centro) → ll3

AI Drawing Prompt Reference

Draw a modular section of a cube focusing on triangles. Start by creating a circle on the base plane and derive points from it, then rotate to form the cube's faces. Identify midpoints of faces and line segments, connecting them to form triangles. Translate these triangles using vectors and draw lines between midpoints to complete the geometric illustration with multiple triangles and cube faces.
The prompt above was compiled from the original drawing commands and is for reference only.