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Cube Cross Sections

Cube Cross Sections
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2020-05-27 07:42
VectorCoordinate GeometrySolid GeometryParametric Equation
This example demonstrates the variety of cross-sectional shapes obtained by slicing a cube at different positions and angles. It involves core math concepts like solid geometry, 3D vectors, parametric curves, and coordinate geometry. Constructed using GeoGebra commands such as Point, Cube, and IntersectPath, with objects like points A-F, cube faces, edges, and intersection paths. Ideal for high school students and math enthusiasts exploring 3D geometry and cross-section properties.

GeoGebra Commands & Parameters

  1. Point(Circle[(1, -1, -1), Distance[(-1, -1, -1), (1, -1, -1)], Segment[(-1, -1, -1), (1, -1, -1)]]) → A
  2. Cube((-1, -1, -1), (1, -1, -1), A) → a, B, faceABFE, faceCDEF, edge2, edge1, edge4, edgeAB, edge3, edgeBF, edgeCF, edgeCD, C, edge5, edgeDE, edgeAE, edgeEF, D, E, F, face1, face3, face2, face4
  3. IntersectPath(eq1, a) → poly1, G, i, j, k, H, I, J, K, L, f, g, h

AI Drawing Prompt Reference

Draw a cube and display various cross-sectional shapes obtained by slicing it at different positions and angles, including points, cube faces, edges, and intersection paths to illustrate core concepts of solid geometry, 3D vectors, parametric curves, and coordinate geometry.
The prompt above was compiled from the original drawing commands and is for reference only.