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Cross Section of a Rectangular Prism

Cross Section of a Rectangular Prism
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2020-03-06 02:51
Coordinate GeometrySolid GeometryGeometric Construction
In collections Cross Sections
This example demonstrates the cross section of a rectangular prism. Key mathematical concepts include the properties of cross sections in solid geometry. Using GeoGebra commands such as Polygon, Point, Prism, etc., the construction of the rectangular prism and its cross section is illustrated. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Polygon(R, C_1, T, S) → q1, r_1, c_1, t, s
  2. Point(xAxis) → V
  3. Polygon(U, P, Q, W) → t1, m, n, q, r
  4. Prism(q1, a) → ThePrism, Z, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, A_1, B_1, D_1, face1, face2, face3, face4, face5
  5. Point(xAxis) → A
  6. Point(zAxis) → O
  7. Point(xAxis) → K
  8. Point(yAxis) → J
  9. Point(xAxis) → I
  10. Plane(I, K, O) → b
  11. Plane(I, J, K) → p
  12. PointIn(b) → CenterOfNormalAngle
  13. Circle(CenterOfNormalAngle, 0.25, b) → d
  14. Line(CenterOfNormalAngle, xAxis) → g
  15. Point(yAxis) → B
  16. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  17. Intersect(xAxis, yAxis) → M
  18. OrthogonalLine(CenterOfNormalAngle, g, b) → h
  19. Intersect(g, d) → i_1, i_2
  20. CircleArc(CenterOfNormalAngle, i_1, i_2, b) → ArcForPlaneAngle
  21. Point(ArcForPlaneAngle) → NormalAngleHandle
  22. Segment(CenterOfNormalAngle, NormalAngleHandle) → NormalSeg
  23. PointIn(ThePrism) → SliceChooser
  24. OrthogonalPlane(SliceChooser, NormalSeg) → PerPenPlane
  25. IntersectPath(PerPenPlane, ThePrism) → CrossSection, D, k, l, e, E, F, G, H, E_1, f, i, j
  26. PointIn(PerPenPlane) → N

AI Drawing Prompt Reference

Draw a rectangular prism with a rectangular base in a 3D coordinate system. Place several points on the coordinate axes)Skip. Construct two auxiliary planes: one through three axis points, another through three different axis points. On the first plane, draw a small circle and a line through its center parallel to an axis. Find the circle-line intersections and create an arc between them. Place a point on this arc and connect it to the circle center to form a normal direction segment. Choose a point inside the prism, then construct a plane through this point perpendicular to the normal segment. This plane intersects the prism, producing a polygonal cross-section. Finally, place an additional point on this cutting plane.
The prompt above was compiled from the original drawing commands and is for reference only.