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Intersection Line of Cylinder and Plane

Intersection Line of Cylinder and Plane
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2021-12-21 21:02
TrigonometrySolid Geometry
In collections Open Middle: Distance, Midpoint, Slope (2)
This example demonstrates the intersection line formed when a cylinder intersects a plane. Key mathematical concepts include cylinder, plane, intersection line, and trigonometric functions. Using GeoGebra commands such as PointIn, Segment, Intersect, etc., a dynamic graphical representation of the intersection is constructed. Suitable for high school mathematics education and learning solid geometry.

GeoGebra Commands & Parameters

  1. PointIn(e) → A
  2. PointIn(e) → B
  3. PointIn(e) → C
  4. Textfield(f) → InputBox1
  5. Textfield(g) → InputBox2
  6. Textfield(h) → InputBox3
  7. Textfield(i) → InputBox4
  8. Textfield(j) → InputBox5
  9. Segment(A, B) → k
  10. Midpoint(k) → D
  11. Segment(A, D) → l
  12. Segment(D, B) → m
  13. Intersect(p, eq1) → E
  14. Polygon(A, E, B) → t1, b_1, a_1, e_1
  15. Angle(B, E, A) → α
  16. Segment(A, E) → n
  17. Segment(E, B) → q
  18. If(C ≟ D, "√", "X") → text6
  19. Mode(l1) → l2
  20. If(c2, "√", "X") → text8
  21. If(c3, "√", "X") → text9
  22. If(Length[l2] ≟ 0, "No digits repeat!", "Repeated digits exist.") → text7

AI Drawing Prompt Reference

Draw the intersection line formed when a cylinder intersects a plane. Start by marking two points on the curve, then connect them to form a line segment. Find the midpoint of this segment and draw two line segments from the midpoint to each endpoint. The intersection points of these segments with the curve form a triangle. Finally, measure one angle of the triangle and display some text based on certain conditions.
The prompt above was compiled from the original drawing commands and is for reference only.