MathPlotAI Logo MathPlotAI

Cutting a Cube with an Interactive Plane

Cutting a Cube with an Interactive Plane
Loading the math board and drawing, please wait…
2020-04-13 16:23
Coordinate GeometrySolid GeometryGeometric Construction
In collections Cutting solids by a plane
This example demonstrates how to use an interactive plane to cut a cube, showing the intersection sections of the cube. Key mathematical concepts include the intersection of a plane and a solid in solid geometry. Using GeoGebra commands such as Point, Cube, and Plane, the construction of the cube and its cutting plane is illustrated. Suitable for middle school and above students to learn solid geometry.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, arêteAD, arêteAB, arêteBC, arêteCD, arêteAE, arêteDH, arêteEH, arêteEF, E, arêteBF, arêteFG, arêteCG, arêteGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Midpoint(C, A) → I
  4. Midpoint(F, H) → J
  5. Line(J, I) → f
  6. Circle(I, Distance[A, B], f) → c
  7. Point(c) → K
  8. Midpoint(F, C) → M
  9. Mirror(K, I) → K'
  10. Line(K', K) → g
  11. Circle(I, (1.2 * Distance[A, B]), g) → d
  12. Point(d) → L
  13. Plane(L, K, K') → p
  14. Circle(K', L, K) → e
  15. Center(e) → N
  16. OrthogonalLine(N, p) → h
  17. Point(h) → O
  18. Vector(N, O) → u
  19. Translate(p, u) → p'
  20. Segment(K', K) → b
  21. Line(L, b) → f_1
  22. Point(arêteEF) → D_1
  23. OrthogonalLine(K, p) → h_1
  24. Plane(K', h_1) → p_1
  25. OrthogonalLine(K, p_1) → k_1
  26. Line(K', k_1) → l_1
  27. Intersect(f_1, l_1) → E_1
  28. Intersect(k_1, f_1) → F_1
  29. Mirror(F_1, K) → G_1
  30. Mirror(E_1, K') → H_1
  31. Polygon(F_1, E_1, H_1, G_1) → q2, m_1, e_1, n_1, q_1
  32. Translate(q2, u) → q2'
  33. IntersectPath(p', a) → poly1, P, l, t, m, Q, R, S, A_1, T, i, j, k