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Cross Section of a Cube

Cross Section of a Cube
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2020-02-27 02:38
Coordinate GeometrySolid GeometryGeometric Construction
In collections Cross Sections
This example demonstrates the cross section of a cube. Key mathematical concepts include solid geometry, specifically plane section. Using GeoGebra commands such as Point, Plane, PointIn, Cube, Intersect, etc., the construction of a cube and its cross-section is illustrated. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(zAxis) → O
  3. Point(xAxis) → K
  4. Point(yAxis) → J
  5. Point(xAxis) → I
  6. Plane(I, K, O) → b
  7. Plane(I, J, K) → p
  8. PointIn(b) → CenterOfNormalAngle
  9. Circle(CenterOfNormalAngle, 0.25, b) → d
  10. Line(CenterOfNormalAngle, xAxis) → g
  11. Point(yAxis) → B
  12. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  13. Cube(A, B, C) → TheCube, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  14. Intersect(xAxis, yAxis) → M
  15. PointIn(TheCube) → SliceChooser
  16. OrthogonalLine(CenterOfNormalAngle, g, b) → h
  17. Intersect(g, d) → i_1, i_2
  18. CircleArc(CenterOfNormalAngle, i_1, i_2, b) → ArcForPlaneAngle
  19. Point(ArcForPlaneAngle) → NormalAngleHandle
  20. Segment(CenterOfNormalAngle, NormalAngleHandle) → NormalSeg
  21. OrthogonalPlane(SliceChooser, NormalSeg) → PerPenPlane
  22. IntersectPath(PerPenPlane, TheCube) → CrossSection_1, N, k, l, m, P, Q, R, S, T, f, i, j

AI Drawing Prompt Reference

Draw a cube and show its cross-section with the x-axis and y-axis. Start by creating point A on the x-axis and point O on the z-axis, then create planes b and p. Next, create point CenterOfNormalAngle on plane b and draw circle d. Draw line g connecting A and the x-axis, then create point B on the y-axis and point C on circle B. Use points A, B, and C to create cube TheCube. Find the intersection point M of the x-axis and y-axis, and select a cross-section SliceChooser from TheCube. Create circular arc ArcForPlaneAngle using the intersection points i_1 and i_2 of line g and circle d, and create point NormalAngleHandle on arc ArcForPlaneAngle. Finally, create a plane PerPenPlane perpendicular to NormalSeg and find its intersection with TheCube to get cross-section CrossSection_1.
The prompt above was compiled from the original drawing commands and is for reference only.