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Curve Stitching on a Cube

Curve Stitching on a Cube
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2018-07-26 17:54
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates curve stitching on a cube. It involves core concepts of cube, geometric construction, and coordinate geometry. Using GeoGebra commands such as Point, Cube, Sequence, Intersect, Line, Mirror, etc., a series of segments and curves are constructed. Suitable for middle school and above students or teachers for geometry teaching and exploration.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Sequence(B + (w * (F - B)), w, 0, 1, 1 / 40) → L_1
  4. Sequence(F + (w * (G - F)), w, 0, 1, 1 / 40) → L_2
  5. Sequence(Segment[Element[L_1, w], Element[L_2, w]], w, 1, 40) → L_3
  6. Sequence(Rotate[L_3, (w * π / 2), xAxis], w, 1, 4) → L_4
  7. Intersect(zAxis, yAxis) → I
  8. Line(I, F) → f
  9. Sequence(Rotate[L_4, ((w * 2) * π / 3), f], w, 1, 3) → L_5
  10. Mirror(L_5, (0, 0, 0)) → L_6