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Cross Section of a Square Pyramid by Steve Phelps

Cross Section of a Square Pyramid by Steve Phelps
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2018-03-17 06:56
TriangleCoordinate GeometrySolid GeometryTransformationGeometric Construction
This example demonstrates the changing cross-section shapes of a square pyramid at different angles. Core math concepts include solid geometry, triangles, Pythagorean theorem, trapezoids, and transformations. Construction highlights involve commands like Point, Pyramid, Translate, and IntersectPath in GeoGebra. Suitable for high school students learning about solid geometry, geometric transformations, and cross-section analysis.

GeoGebra Commands & Parameters

  1. Point(Circle[(2, -2, -2), Distance[(-2, -2, -2), (2, -2, -2)], Segment[(-2, -2, -2), (2, -2, -2)]]) → A
  2. Pyramid((-2, -2, -2), (2, -2, -2), (2, 2, -2), (-2, 2, -2), (0, 0, 2)) → a, face1, edge5, edge6, edge7, edge8, face2, face3, face4, face5, edge1, edge2, edge3, edge4
  3. Translate(Rotate[Rotate[Plane[(0, 1, 0), xAxis], tilt, xAxis], turn, zAxis], Vector[(0, 0, shift)]) → b
  4. IntersectPath(b, a) → poly1, G, i, j, k, H, I, J, K, L, f, g, h