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Cube Geometry: Shortest Path

Cube Geometry: Shortest Path
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2017-06-05 00:04
VectorSolid GeometryGeometric Construction
This applet shows a net of a cube with two points on adjacent faces and the shortest path between them. It demonstrates the geometric properties of a cube and the concept of the shortest path. The construction uses points, cubes, planes, and vectors in GeoGebra. Suitable for middle school and above students to learn about cube geometry.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. PointIn(faceEFGH) → I
  6. PointIn(faceABFE) → J
  7. OrthogonalPlane(J, edgeEF) → b
  8. OrthogonalPlane(I, edgeEF) → c
  9. Intersect(edgeEF, b) → K
  10. Intersect(edgeEF, c) → L
  11. OrthogonalPlane(J, edgeBF) → d
  12. IntersectPath(c, d) → e
  13. OrthogonalPlane(I, edgeFG) → f_1
  14. IntersectPath(f_1, d) → g
  15. Intersect(e, faceABFE) → M
  16. Segment(J, M) → h
  17. Segment(M, L) → i
  18. Segment(L, I) → j
  19. Vector(L, K) → u
  20. Segment(J, N) → k
  21. Segment(N, I) → l
  22. Polygon(B, A, 4, xOyPlane) → poly1, m, n, p, q, f, P
  23. Polygon(P, f, 4, xOyPlane) → poly2, r, s, t, a_1, O, Q
  24. Polygon(A, D, 4, xOyPlane) → poly3, b_1, c_1, d_1, e_1, R, S
  25. Polygon(C, B, 4, xOyPlane) → poly4, g_1, h_1, i_1, j_1, T, U
  26. Polygon(D, C, 4, xOyPlane) → poly5, k_1, l_1, m_1, n_1, V, W
  27. Circle(edgeAB, J) → q_1
  28. Intersect
  29. Intersect(xOyPlane, q_1) → C_1, D_1
  30. Circle(edgeEF, I) → p_1
  31. Plane(A, E, F) → o
  32. Intersect(o, p_1) → Z, A_1
  33. Circle(edgeAB, A_1) → r_1
  34. Intersect(xOyPlane, r_1) → B_1, E_1
  35. Segment(D_1, E_1) → s_1