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Stitching in a Cube

Stitching in a Cube
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2016-03-05 18:51
Coordinate GeometrySolid GeometryGeometric Construction
This example analyzes stitching lines in a cube. Key mathematical concepts include faces and edges in solid geometry. Using GeoGebra commands such as Point, Cube, Intersect, etc., the various faces and edges of the cube are constructed. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Point(Circle[B_1, Distance[A, B_1], Segment[A, B_1]]) → C_1
  2. Cube(A, B_1, C_1) → a, D_1, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E_1, edgeBF, edgeFG, edgeCG, edgeGH, F_1, G_1, H_1, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Circle(xAxis, G_1) → c
  4. Intersect(zAxis, c) → I, J
  5. CircleArc(A, G_1, I) → d
  6. Point(d) → G
  7. Angle(G_1, A, G) → α
  8. Line(G, A) → b
  9. Rotate(a, α, xAxis) → a'
  10. Rotate(B_1, α, xAxis) → B
  11. Rotate(C_1, α, xAxis) → C
  12. Rotate(D_1, α, xAxis) → D
  13. Rotate(E_1, α, xAxis) → E
  14. Rotate(F_1, α, xAxis) → F
  15. Rotate(H_1, α, xAxis) → H
  16. Segment(A, B) → e
  17. Segment(B, C) → f
  18. Segment(C, D) → g
  19. Segment(D, A) → h
  20. Segment(E, F) → i
  21. Segment(F, G) → j
  22. Segment(H, E) → l
  23. Segment(E, A) → m
  24. Segment(F, B) → n
  25. Segment(G, C) → p_1
  26. Segment(H, D) → q
  27. Sequence(C + (k * (B - C)), k, 0, 1, 0.1) → CB
  28. Sequence(F + (k * (E - F)), k, 0, 1, 0.1) → FE
  29. Sequence(H + (k * (D - H)), k, 0, 1, 0.1) → HD
  30. Sequence(Segment[Element[CB, k], Element[FE, k]], k, 1, 11) → list1
  31. Sequence(Segment[Element[FE, k], Element[HD, k]], k, 1, 11) → list2
  32. Sequence(Segment[Element[HD, k], Element[CB, k]], k, 1, 11) → list3
  33. Polygon(Element[CB, p], Element[FE, p], Element[HD, p]) → poly1, r, s, t
  34. Segment(H, G) → k
  35. Vector(C, C + ((p - 1) / 10 * (B - C))) → u
  36. Vector(F, F + ((p - 1) / 10 * (E - F))) → v
  37. Vector(H, H + ((p - 1) / 10 * (D - H))) → w