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Exploring Sections of Cubes by math

Exploring Sections of Cubes by math
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2018-10-29 16:36
FunctionSolid GeometryCalculusLimitGeometric Construction
This example demonstrates the changes in cross-sectional shapes when a cube is sliced at different angles. It involves core mathematical concepts such as solid geometry, cross-section geometry, quadratic functions, logarithmic functions, and limits. The construction uses GeoGebra commands like Cube, Polygon, PointIn, Translate, Rotate, Point, Plane, IntersectPath, and OrthogonalLine. Suitable for high school students and math enthusiasts to understand spatial geometry and function applications.

GeoGebra Commands & Parameters

  1. Cube((-1.5, -1.5, 0), (1.5, -1.5, 0), xOyPlane) → m, M, face4, face5, face6, edge1, edge2, edge3, edge4, edge5, edge6, edge7, N, edge8, edge9, edge10, edge11, edge12, Q, R, S, T, face1, face2, face3
  2. Polygon(B + (-2, -2), B + (2, -2), B + (2, 2), B + (-2, 2)) → poly3, e, f, g, i
  3. PointIn(poly3) → C
  4. Translate((0, 0, 0), Vector[B, C]) → A
  5. Polygon(A + (-4, -4), A + (4, -4), A + (4, 4), A + (-4, 4)) → poly1, a, b, c, d
  6. Rotate(Rotate[Translate[poly1, Vector[A, A + (0, 0, h)]], (90° * s), A + (0, 0, h), yAxis], (90° * t), A, zAxis) → poly2
  7. Rotate(D, 120°, (0, 0, 0)) → E
  8. Polygon(D, E, 3, xOyPlane) → poly4, j, k, l, F
  9. Point(list1) → G
  10. Point(list2) → H
  11. Point(list3) → I
  12. Plane(G, I, H) → n
  13. IntersectPath(n, m) → poly6, poly5, V, p, q, r, a_1, b_1, c_1, e_1, f_1, poly7, K, L_1, O, P, J, L, U
  14. Rotate(m, 0, zAxis) → m'
  15. Rotate(m, 0, zAxis) → m'_1
  16. OrthogonalLine(A, n) → d_1