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The Infernal Pyramid

The Infernal Pyramid
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2017-12-12 20:23
TriangleFunctionCoordinate GeometrySolid GeometryDerivative
This example demonstrates the construction of a pyramid. Key mathematical concepts include power functions, standard deviation, isosceles triangles, and derivatives. Using GeoGebra commands such as Pyramid, Point, and Plane, an isosceles triangle pyramid can be constructed. Suitable for high school mathematics education, particularly in coordinate geometry and solid geometry.

GeoGebra Commands & Parameters

  1. Pyramid(A, C, B, D) → a, faceABC, edgeBD, faceACD, faceBCD, faceABD, edgeAC, edgeBC, edgeAB, edgeAD, edgeCD
  2. Point(Segment[(0, 0, sqrt(2) / 2), A]) → E
  3. Plane((0, -1, 0), (0, 1, 0), E) → b
  4. IntersectPath(b, a) → poly1, F, G, H, I, f, g, h, i
  5. Segment(K, J) → j
  6. Segment(K, A) → k
  7. Segment(L, E) → l

AI Drawing Prompt Reference

Draw an isosceles triangular pyramid with base triangle ABC and apex D. First, construct the base triangle ABC, then establish the apex D. Use the Pyramid command to build the pyramid. On triangle ABC, take a point E, and create a plane b through E and A, which intersects the pyramid's faces to form polygon poly1 and points F, G, H, and I. Finally, connect points K and J, K and A, and L and E to form the pyramid's edges.
The prompt above was compiled from the original drawing commands and is for reference only.