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Cube Division Demonstration by Diego Lieban (5)

Cube Division Demonstration by Diego Lieban (5)
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2019-01-21 16:36
Coordinate GeometrySolid GeometryCalculusGeometric Construction
In collections Dissecting a cube into equal parts
This example demonstrates the geometric construction of dividing a cube into two parts. It involves core mathematical concepts such as solid geometry, coordinate geometry, integral calculus, and function graphing. Key GeoGebra commands and objects used in the construction include Intersect, Point, Polygon, Prism, OrthogonalLine, Rotate, Circle, Vector, and Translate. It is suitable for high school and above students learning spatial geometry, calculus, and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → B
  2. Point(yAxis) → D
  3. Polygon(B, C, A, D) → q1, b, c, a, d
  4. Prism(q1, 1) → e, E, edgeBE, edgeCF, edgeAG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceBCFE, faceACFG, faceADHG, faceBDHE, faceEFGH
  5. Polygon(H, I, J, K) → q2, h, i, j, k
  6. Prism(q2, 1) → f, L, edgeHL, edgeIM, edgeJN, edgeKO, edgeLM, edgeMN, edgeNO, edgeLO, M, N, O, faceHIML, faceIJNM, faceJKON, faceHKOL, faceLMNO
  7. Point(c) → P
  8. OrthogonalLine(P, xOyPlane) → g
  9. Rotate(e, 180°, g) → e'
  10. Rotate(f, 180°, g) → f'
  11. Circle(C, r) → p
  12. Intersect(p, xAxis, 2) → Q
  13. Vector(C, Q) → u
  14. Translate(e', u) → e''
  15. Translate(f', u) → f''