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Space Diagonal Example

Space Diagonal Example
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2015-09-05 01:18
Coordinate GeometrySolid GeometryGeometric Construction
This example illustrates the concept of space diagonal. Key mathematical concepts include space diagonals in solid geometry. Using GeoGebra commands such as Intersect, Point, Polygon, etc., a cube is constructed to demonstrate how to create space diagonals. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xAxis) → A
  2. Point(yAxis) → B
  3. Point(xAxis) → D
  4. Polygon(A, B, C, D) → poly1, a, b, c, d
  5. Point(zAxis) → H
  6. Prism(A, B, C, D, H) → e, E, edgeAB, edgeBC, edgeCD, edgeAD, edgeAH, edgeBE, edgeCF, edgeDG, edgeEH, edgeEF, F, edgeFG, edgeGH, G, faceABCD, faceABEH, faceBCFE, faceCDGF, faceADGH, faceEFGH
  7. Intersect(edgeDG, d) → I
  8. Intersect(edgeEF, edgeBE) → J
  9. Segment(I, J) → f
  10. Intersect(b, a) → K
  11. Segment(I, K) → g
  12. Polygon(J, K, I) → poly2, i, j, k

AI Drawing Prompt Reference

Draw a cube and highlight its space diagonal. Start by creating the base of the cube, then extend it upward to form the full cube. Next, identify the intersection points of the space diagonals with the coordinate axes and connect these points to form the diagonals. Finally, emphasize the space diagonals to clearly illustrate the concept.
The prompt above was compiled from the original drawing commands and is for reference only.