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Cube Net and Shadow

Cube Net and Shadow
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2016-02-04 04:48
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates a cube's net and its shadow on a plane. Key mathematical concepts include solid geometry and projection. Using GeoGebra commands such as Circle, OrthogonalLine, Intersect, etc., the cube and its net can be constructed. Suitable for middle school and above students to learn about solid geometry and projection.

GeoGebra Commands & Parameters

  1. Circle(A, r, zAxis) → c
  2. OrthogonalLine(B, xOyPlane) → a
  3. OrthogonalLine(C, xOyPlane) → b
  4. Intersect(a, c) → D,
  5. Intersect(b, c) → E,
  6. Segment(D, E) → d
  7. Circle(D, r, a) → e
  8. Circle(E, r, b) → f
  9. Line(D, xAxis) → g
  10. Line(E, xAxis) → h
  11. Intersect(g, e) → V03, V10
  12. Intersect(h, f) → V04, V07
  13. Point(Circle[V04, Distance[V03, V04], Segment[V03, V04]]) → J
  14. Cube(V03, V04, J) → i, K, faceJKON, faceLMNO, edgeFK, edgeFH, edgeHJ, edgeJK, edgeFL, edgeKO, edgeLO, edgeLM, L, edgeHM, edgeMN, edgeJN, edgeNO, M, N, O, faceFHJK, faceFKOL, faceFHML, faceHJNM
  15. Net(i, Net) → k, P, V01, V05, V06, V08, V09, facePQRS, facePSUT, face1, face2, face3, Q, faceTUVW, edgePS, edgePQ, edgeQR, edgeRS, edgeSU, edgeTU, edgePT, edgePZ, edge6, R, edge1, edge2, edge7, edge3, edge4, edge8, edge5, edgeUV, edgeVW, edgeTW, S, V14, V11, V12, V13, V02
  16. Ray(Foco, V01) → j
  17. Ray(Foco, V02) → l
  18. Ray(Foco, V03) → m
  19. Ray(Foco, V04) → n
  20. Intersect(j, xOyPlane) → VP02
  21. Intersect(l, xOyPlane) → VP03
  22. Intersect(m, xOyPlane) → VP01
  23. Intersect(n, xOyPlane) → VP04
  24. Ray(Foco, V05) → p
  25. Ray(Foco, V06) → q
  26. Ray(Foco, V07) → s
  27. Intersect(s, xOyPlane) → VP07
  28. Intersect(q, xOyPlane) → VP06
  29. Intersect(p, xOyPlane) → VP05
  30. Ray(Foco, V08) → t
  31. Ray(Foco, V09) → a_1
  32. Ray(Foco, V10) → b_1
  33. Intersect(t, xOyPlane) → VP08
  34. Intersect(a_1, xOyPlane) → VP09
  35. Intersect(b_1, xOyPlane) → VP10
  36. Ray(Foco, V11) → c_1
  37. Ray(Foco, V12) → d_1
  38. Ray(Foco, V13) → e_1
  39. Ray(Foco, V14) → f_1
  40. Intersect(c_1, xOyPlane) → VP11
  41. Intersect(d_1, xOyPlane) → VP12
  42. Intersect(e_1, xOyPlane) → VP13
  43. Intersect(f_1, xOyPlane) → VP14
  44. Polygon(VP06, VP05, VP04, VP07) → poly1, vp06, vp05, vp04, vp07
  45. Polygon(VP04, VP02, VP03, VP01) → poly2, vp04_1, vp02, vp03, vp01
  46. Polygon(VP07, VP04, VP01, VP10) → poly3, vp07_1, vp04_2, vp01_1, vp10
  47. Polygon(VP10, VP01, VP14, VP11) → poly4, vp10_1, vp01_2, vp14, vp11
  48. Polygon(VP11, VP14, VP13, VP12) → poly5, vp11_1, vp14_1, vp13, vp12
  49. Polygon(VP08, VP07, VP10, VP09) → poly6, vp08, vp07_2, vp10_2, vp09

AI Drawing Prompt Reference

Draw a cube and its net, and then draw the projection of the cube on a plane, including four vertices and four polygons.
The prompt above was compiled from the original drawing commands and is for reference only.