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Shortest Path on an Outside Corner

Shortest Path on an Outside Corner
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2017-07-12 00:53
AngleFunctionOptimization
In collections Cuboids & their Nets
This example demonstrates finding the shortest path in a geometric figure at an outside corner. Key mathematical concepts include angles and path length. Using GeoGebra commands such as Point, Intersect, Polygon, Rotate, etc., a dynamic geometric figure is constructed to illustrate how to find the shortest path under given conditions. Suitable for middle school and above students to learn geometric construction and optimization.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(yAxis, zAxis) → B
  3. Point(zAxis) → C
  4. Polygon(A, B, C, D) → poly1, a, b, c, d
  5. Rotate(poly1, (-(90°)), zAxis) → poly1'
  6. Polygon((-4, 0, 0), (0, 0, 0), (0, 4, 0), (4, 4, 0), (4, -4, 0), (-4, -4, 0)) → poly2, f, g, h, i, j, k
  7. PointIn(poly2) → E
  8. PointIn(poly1') → F
  9. Rotate(F, (-(90°)), b) → F'
  10. Rotate(F', (-(90°)), f) → F''
  11. Line(E, F'') → l
  12. Rotate(F, (-(90°)), g) → F'_1
  13. Line(E, F'_1) → n
  14. Intersect(n, g) → I
  15. Intersect(l, f) → G
  16. Segment(G, F') → m
  17. Intersect(m, b) → H
  18. PolyLine(E, G, H, F) → p
  19. Intersect(b, poly2) → J
  20. PolyLine(E, J, F) → q
  21. PolyLine(E, I, F) → r

AI Drawing Prompt Reference

Draw a geometric figure with a quadrilateral poly1 and a hexagon poly2. Select a point E inside the hexagon and a point F inside the quadrilateral. Through rotation and intersection operations, find the shortest path between the quadrilateral and the hexagon. First, rotate point F, then draw lines from E through the rotated points to find intersection points I and G. Connect E, G, H, and F to form path p, and connect E, J, and F to form path q, and E, I, and F to form path r.
The prompt above was compiled from the original drawing commands and is for reference only.