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Sun's Path and House Shadow

Sun's Path and House Shadow
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2015-03-22 17:45
Coordinate GeometrySolid GeometryGeometric Construction
In collections GeoGebra 3D Grafikrechner mit AR - Beispielsammlung
This example demonstrates the geometric relationship between the sun's path and the shadow of a house. It involves core mathematical concepts such as conditional probability, diagrams, correlation, right triangles, polygons, and quadrilaterals. The construction utilizes GeoGebra commands/objects like Polygon, Prism, Pyramid, Sphere, Rotate, OrthogonalPlane, IntersectPath, Point, Line, Segment, Intersect, CircleArc, ConvexHull, etc. It is suitable for high school students studying solid geometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → Vieleck1, a, b, c, d
  2. Prism(Vieleck1, 2) → e, E, KanteAE, KanteBF, KanteCG, KanteDH, KanteEF, KanteFG, KanteGH, KanteEH, F, G, H, FlächeABFE, FlächeBCGF, FlächeCDHG, FlächeADHE, FlächeEFGH
  3. Pyramid(FlächeEFGH, 1.4173117127901385) → f, I, FlächeEFI, FlächeFGI, FlächeGHI, FlächeEHI, KanteEI, KanteFI, KanteGI, KanteHI
  4. Sphere(MP, R) → n
  5. Rotate(zAxis, (-(90° - Breite)), yAxis) → achse
  6. OrthogonalPlane(P, achse) → ekl
  7. IntersectPath(ekl, n) → k
  8. Point(k) → S
  9. Line(S, MP) → s
  10. Line(I, s) → s_1
  11. Segment(sW, nW) → m
  12. Intersect(xOyPlane, k) → West, Ost
  13. CircleArc(P, West, Ost, achse) → p
  14. Line(G, s) → s_3
  15. Line(H, s) → s_2
  16. Line(F, s) → s_4
  17. Line(E, s) → s_5
  18. Intersect(s_2, xOyPlane) → L
  19. Intersect(s_5, xOyPlane) → M
  20. Intersect(s_3, xOyPlane) → N
  21. Intersect(s_4, xOyPlane) → O
  22. Intersect(s_1, xOyPlane) → K
  23. ConvexHull(LP) → Graph1
  24. Polygon(First[Graph1, Length[Graph1]]) → poly1
  25. Intersect(s, xOyPlane) → Q
  26. Angle(J, MP, S) → α

AI Drawing Prompt Reference

Draw a geometric model of a house showing the relationship between the sun's path and the house's shadow. Start by constructing a quadrilateral house, extend it upward to form a prism, then transform the top face into a pyramid. Place a sphere to represent the sun and rotate a plane to intersect its path perpendicularly, marking the intersection as the sun's position. Draw lines from the sun's position to the house's vertices, intersecting the ground to create several points. Connect these points to form a convex hull, then draw an arc representing the sun's trajectory and a polygon for the ground shadow, labeling the angle between the sun and the house's top vertex.
The prompt above was compiled from the original drawing commands and is for reference only.