MathPlotAI Logo MathPlotAI

Moving Cube Cross Section

Moving Cube Cross Section
Loading the math board and drawing, please wait…
2016-07-30 04:09
Solid GeometryGeometric Construction
This example demonstrates the changing shape of a cube's cross-section as it moves. Key math concepts include solid geometry, area calculation, and cross-section analysis. Construction highlights the use of commands like Sphere, Intersect, PointIn, IntersectConic, Point, Segment, OrthogonalPlane, Plane, OrthogonalLine, Circle, Line, Polygon, Prism, and IntersectPath in GeoGebra. Suitable for high school and above students studying 3D geometry and visualization.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), b) → c
  2. Intersect(zAxis, xAxis) → B
  3. PointIn(c) → A
  4. Sphere(A, d) → e
  5. IntersectConic(c, e) → f
  6. Point(f) → C
  7. Segment(A, C) → g
  8. OrthogonalPlane(A, g) → h
  9. Intersect(h, f) → D, E
  10. Segment(A, D) → i
  11. Segment(A, E) → j
  12. Plane(A, E, C) → k
  13. OrthogonalLine(E, j, space) → l
  14. Circle(A, (d * sqrt(2)), i) → p
  15. Line(E, i) → m
  16. Line(C, i) → n
  17. Circle(E, d, k) → q
  18. Intersect
  19. Intersect(p, q) → F, G, ,
  20. Polygon(A, E, F, C) → poly1, a_1, e_1, f_1, c_1
  21. Prism(poly1, d) → o, H, edgeAH, edgeEI, edgeFJ, edgeCK, edgeHI, edgeIJ, edgeJK, edgeHK, I, J, K, faceAEIH, faceEFJI, faceCFJK, faceACKH, faceHIJK
  22. IntersectPath(b_1, o) → poly2, L, g_1, M, N, O, P, r, s, t, d_1