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Square Pyramid by Angel Rivas

Square Pyramid by Angel Rivas
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2016-05-14 02:46
PolygonCoordinate GeometrySolid GeometryCalculusGeometric Construction
This example demonstrates the 3D geometric shape and structure of a square pyramid. Core math concepts include solid geometry, polygon (square base), linear equations, summation operations (upper and lower sums), and kite properties. Construction highlights involve GeoGebra commands/objects like Polygon, Pyramid, Net, and PointIn. Suitable for high school students learning solid geometry, spatial visualization, and geometric constructions.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4, xOyPlane) → poly1, f, g, h, i, C, D
  2. Pyramid(poly1, b) → c, F, faceABF, faceBCF, faceCDF, faceADF, edgeAF, edgeBF, edgeCF, edgeDF
  3. Net(c, a) → d, E, faceEGJ, faceGHK, faceHIL, faceEIM, edgeEG, edgeGH, edgeHI, edgeEI, edgeEJ, edgeGJ, G, edgeGK, edgeHK, edgeHL, edgeIL, edgeIM, edgeEM, H, I, J, K, L, M, faceEGHI
  4. PointIn(faceHIL) → PointfaceHIL
  5. PointIn(faceEGHI) → PointfaceEGHI
  6. PointIn(faceEIM) → PointfaceEIM
  7. PointIn(faceEGJ) → PointfaceEGJ
  8. PointIn(faceGHK) → PointfaceGHK

AI Drawing Prompt Reference

Draw a right square pyramid with a square base lying on a horizontal plane and an apex directly above the center of the base. Start by sketching the square base, then connect the apex to each corner of the base to form four triangular lateral faces and four edges. Next, create a net of the pyramid, consisting of the square base and four triangles arranged around it, maintaining correspondence with the 3D shape. Place one point inside each of the five faces of the net (four triangles and the square) to mark them. The final image should clearly show both the solid pyramid and its flattened net with interior points.
The prompt above was compiled from the original drawing commands and is for reference only.