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Intersection of a Circle and a Prism

Intersection of a Circle and a Prism
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2017-09-08 13:32
Coordinate GeometrySolid GeometryGeometric Construction
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates the intersection of a circle and a prism. Key mathematical concepts include solid geometry and coordinate geometry. Using GeoGebra commands such as IntersectPath, Point, and Locus, the intersection of a circle and a prism can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. IntersectPath(z = 0, c) → d
  2. Point(d) → A
  3. Locus(B, A) → LlocGeomètric1
  4. Intersect(fcos, xAxis, (0.5585993153125077, 0)) → C
  5. Surface(((R * cos(u)) * sin(v)), ((R * sin(u)) * sin(v)), (R * cos(v)), u, 0, (2 * π), v, 0, π) → b
  6. Sphere((0, 0), R) → g
  7. Surface((((u * R) * cos(t)) * fsin(t)) + (((1 - u) * R) * cos(t)), (((u * R) * sin(t)) * fsin(t)) + (((1 - u) * R) * sin(t)), ((u * R) * fcos(t)), t, x(C), π / 2, u, 0, 1) → l
  8. CurveCartesian(((R * cos(t)) * fsin(t)), ((R * sin(t)) * fsin(t)), (R * fcos(t)), t, 0, (2 * π)) → e
  9. Sequence(CircleArc[(0, 0), POL, e(t), xOyPlane], t, π + x(C), (3 * π / 2), 0.01) → llista2
  10. CurveCartesian((R * cos(t)), (R * sin(t)), 0, t, x(C), π / 2) → n
  11. Sequence(CircleArc[(0, 0), POL, e(t)], t, x(C), π / 2, 0.01) → llista3
  12. Sequence(CircleArc[(0, 0), POL, n(t), xOyPlane], t, π / 2, π + x(C), 0.01) → llista4
  13. Sequence(CircleArc[(0, 0), POL, n(t)], t, (3 * π / 2), (2 * π) + x(C), 0.01) → llista5
  14. CurveCartesian(((R * cos(t)) * fsin(t)), ((R * sin(t)) * fsin(t)), (R * fcos(t)), t, x(C), π / 2) → e1
  15. CurveCartesian(((R * cos(t)) * fsin(t)), ((R * sin(t)) * fsin(t)), (R * fcos(t)), t, π + x(C), (3 * π / 2)) → e2
  16. Surface((((u * R) * cos(t)) * fsin(t)) + ((1 - u) * (((1 - c3(t)) * x(P1)) + (c3(t) * x(P2)))), (((u * R) * sin(t)) * fsin(t)) + ((1 - u) * (((1 - c3(t)) * y(P1)) + (c3(t) * y(P2)))), ((u * R) * fcos(t)), t, x(C), π / 2, u, 0, 1) → o
  17. Angle(P1, (0, 0), P2) → α
  18. Line((0, 0), P1) → q
  19. Segment(P1, P2) → sg
  20. Surface((((u * R) * cos(ang - t)) * fsin(ang - t)) + ((((1 - u) * R) * cos(ang + t)) * fsin(ang + t)), (((u * R) * sin(ang - t)) * fsin(ang - t)) + ((((1 - u) * R) * sin(ang + t)) * fsin(ang + t)), ((u * R) * fcos(ang - t)) + (((1 - u) * R) * fcos(ang + t)), u, 0, 1, t, 0, (2 * π)) → r
  21. Surface(x(P1) + (cos(γ) * ((((u * R) * cos(t)) * fsin(t)) + (((1 - u) * R) * cos(t)) - x(P1))) + (sin(γ) * ((((u * R) * sin(t)) * fsin(t)) + (((1 - u) * R) * sin(t)) - y(P1))), y(P1) - (sin(γ) * ((((u * R) * cos(t)) * fsin(t)) + (((1 - u) * R) * cos(t)) - x(P1))) + (cos(γ) * ((((u * R) * sin(t)) * fsin(t)) + (((1 - u) * R) * sin(t)) - y(P1))), ((u * R) * fcos(t)), t, x(C), π / 2, u, 0, 1) → t
  22. OrthogonalLine(P1, xOyPlane) → f_1
  23. Rotate(n, (-γ), f_1) → n'

AI Drawing Prompt Reference

Draw the intersection of a circle and a prism. First, draw a circle, then draw a prism, find the intersection points between the circle and the prism, and finally construct the intersection shape using these points.
The prompt above was compiled from the original drawing commands and is for reference only.