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Square Cross Section: Building the Sides

Square Cross Section: Building the Sides
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2015-07-27 19:28
PolygonSolid GeometryTransformationGeometric ConstructionGraphing
In collections Square Cross Sections
This example demonstrates how to construct the sides of a cube based on its pre-built edges through linear translation. Key mathematical concepts include: ①the relationship between cross sections and lateral faces in solid geometry; ②application of translation in constructing parallel cross sections; ③parametric representation of polygons and surfaces. Construction details: Use the Polygon command to create base cross-section polygons, apply Surface and CurveCartesian commands to generate lateral curved surfaces, and use Segment commands to connect edge vertices. Suitable for high school and college students learning solid geometry cross-section problems, as well as understanding linear transformations in 3D construction.

GeoGebra Commands & Parameters

  1. Root(f) → R1, R2
  2. Segment(R1, R2) → a
  3. Point(a) → A
  4. Segment(A, B) → b
  5. Polygon(A, B, (x(B), y(B), y(B)), (x(A), y(A), y(B))) → poly1, a_1, b_1, c, d
  6. CurveCartesian(t, 0, f(t), t, 1, 5) → e
  7. CurveCartesian(t, f(t), f(t), t, 1, 5) → g
  8. Surface(u + ((1 - u) * t), (u * 0) + ((1 - u) * 0), (u * 0) + ((1 - u) * f(t)), u, 0, 1, t, 1, 5) → h

AI Drawing Prompt Reference

Create a square cross‑section polygon as the base of a cube. Then generate the cube’s side faces by linearly translating this base polygon along a direction, forming parallel cross‑sectional faces. Connect the corresponding vertices of the base and the translated faces with line segments to outline the edges. Use curved surface commands to draw the lateral surfaces that join the side faces, giving a smooth visual of how the cross sections relate to the solid’s sides. The construction illustrates the relationship between cross sections and lateral faces in solid geometry, the application of translation for building parallel sections, and a parametric representation of polygons and surfaces in three‑dimensional space.
The prompt above was compiled from the original drawing commands and is for reference only.