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Oblique Pyramid Opening 3: Dynamic Geometry Demo

Oblique Pyramid Opening 3: Dynamic Geometry Demo
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2016-12-08 15:04
CirclePolygonCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the construction of an oblique pyramid with an 'opening' effect, showing how the lateral faces change when the apex is shifted off-center in 3D space. Core mathematical concepts include solid geometry (pyramids, oblique vs. right pyramids), polygonal faces and edges, and the Pythagorean theorem for computing lengths or heights. Construction details: using GeoGebra commands such as Point, Cube, Intersect, Pyramid, Circle, and Polygon, the builder first creates a cube framework, then determines the apex via intersections and auxiliary circles, and finally generates lateral faces (e.g., faceADH, faceABH) and edges (edgeDH, edgeAH) using Polygon. This is suitable for high school or early college students to explore 3D geometric construction, and for teachers to illustrate spatial reasoning and pyramid properties.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH_1, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Intersect(edgeEH, edgeDH_1) → I
  6. Pyramid(faceABCD, H) → b, faceADH, faceABH, faceBCH, faceCDH, edgeDH, edgeAH, edgeBH, edgeCH
  7. Circle(edgeCH, B) → c
  8. Point(c) → J
  9. Polygon(J, C, H) → poly1, h, j, c_1

AI Drawing Prompt Reference

Draw an oblique pyramid with an opening effect. Start with a cube framework defined by two points on the coordinate axes and a third point on a circle based on their distance. Use the cube's top edge intersection as the apex, which is off-center. Construct the pyramid's lateral faces from this apex to the cube's base vertices, and keep the base. Then create an auxiliary circle using one lateral edge as diameter, pick a point on it, and form a triangle with that point and two base vertices to show the dynamic side. Emphasize the 3D solid geometry, the oblique nature, and the changing lateral faces.
The prompt above was compiled from the original drawing commands and is for reference only.