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Projection of the Cuboid Diagonal by Anthony OR 柯志明

Projection of the Cuboid Diagonal by Anthony OR 柯志明
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2016-05-18 12:45
VectorCoordinate GeometrySolid Geometry
In collections Projections and Angles
This example demonstrates the projection of the cuboid diagonal. It involves core mathematical concepts such as vectors, coordinate geometry, and solid geometry. The construction uses commands like Translate, Segment, Point, Vector, and Angle in GeoGebra. Suitable for high school and above students to learn about spatial geometry and vector projections.

GeoGebra Commands & Parameters

  1. Translate(Polygon[B, C, H, G], Vector[(0, 0)]) → poly1
  2. Translate(Prism[Polygon[A, A + (5, 0), A + (5, 4), A + (0, 4)], 3], Vector[(0, 0)]) → a
  3. Segment(A, H) → i
  4. Point(Segment[A, B]) → P
  5. Segment(B, H) → f
  6. Segment(A, P) → j
  7. Vector(P, P + (0.7, 0, 0)) → u
  8. Angle(H, B, A) → α

AI Drawing Prompt Reference

Draw a cuboid and show the projection of its diagonal. First, sketch the three visible faces of the cuboid. Then identify the start and end points of the diagonal. Next, draw a line segment starting from the diagonal's endpoint, perpendicular to the diagonal, to represent the projection. Finally, label the relevant angles of the diagonal and projection to illustrate concepts in spatial geometry and vector projection.
The prompt above was compiled from the original drawing commands and is for reference only.