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Core of Four Connected Cylinders

Core of Four Connected Cylinders
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2023-03-01 06:22
Coordinate GeometrySolid GeometryParametric Equation
In collections intersection: surface-surface, curve-curve
This example demonstrates the central part of four connected cylinders. It involves core mathematical concepts such as parametric curves, solid geometry, and quadratic equations. Using GeoGebra commands like Circle, Point, Join, Polygon, Mirror, Surface, and CurveCartesian, this complex geometric figure can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(M_0, r, xOyPlane) → c_0
  2. Point(c_0, 0) → A
  3. Point(c_0, 1 / 4) → B
  4. Join({{M}, Sequence[Point[c_0, j], j, 0, 1 / 4 + 0.01, 0.01]}) → l1
  5. Polygon(l1) → poly1
  6. Mirror(poly1, Line[M, B]) → poly2
  7. Mirror(poly1, Line[A, M]) → poly1'
  8. Mirror(poly2, Line[A, M]) → poly2'
  9. Surface(M_0 + ((r * sin(t)), (r * cos(t)), u - h), t, pi, pi + pi / 2, u, 0, h) → a
  10. Surface(C - ((r * sin(t)), (r * cos(t)), 0) + ((r * sin(k)), (r * cos(k)), 0), t, pi, (3 * pi / 2), k, ((-pi)) / 2, 0) → e
  11. Surface(M_0 + ((r * sin(t)), (r * cos(t)), 0) + (u * (M - (M_0 + ((r * sin(t)), (r * cos(t)), 0)))), t, pi, (pi * 3 / 2), u, 0, 1) → f''
  12. CurveCartesian(M_1 + ((r * cos(t)), (r * sin(t)), 0), t, pi / 2, pi) → r_1
  13. Surface(M_1 + ((r * cos(t)), (r * sin(t)), 0) + (u * ((-M_1) - ((r * cos(t)), (r * sin(t)), 0) + M)), t, pi / 2, pi, u, 0, 1) → f'''
  14. CurveCartesian(M_0 + ((r * sin(t)), (r * cos(t)), 0), t, pi, (pi * 3 / 2)) → r_0
  15. Surface(r_1(t) + (u * (r_0(t + pi / 2) - r_1(t))), t, pi / 2, pi, u, 0, 1) → f
  16. Mirror(f, Line[A, C]) → f'
  17. Mirror(a, Plane[Line[A, C], Line[A, (x(A), y(A), 0)]]) → a'
  18. Surface(M_1 + ((r * sin(t)), (r * cos(t)), u - h), t, ((-pi)) / 2, 0, u, 0, z(M_0)) → b
  19. Mirror(b, Plane[Line[A, C], Line[A, (x(A), y(A), 0)]]) → b''
  20. Circle(M_1, r, xOyPlane) → c_1
  21. Circle(M_3, r, xOyPlane) → c_3
  22. Circle(M_2, r, xOyPlane) → c_2
  23. CurveCartesian(M_2 + ((r * cos(t)), (r * sin(t)), 0), t, 0, pi / 2) → r_2
  24. CurveCartesian(M_3 + ((r * cos(t)), (r * sin(t)), 0), t, (3 / 2 * pi), (2 * pi)) → r_3

AI Drawing Prompt Reference

Draw a central part of four connected cylinders. The figure includes a circular base, a connecting line, a polygon, and two mirrored polygons. The construction order is to first draw the circle and connecting line, then create the polygon, followed by mirroring to generate mirrored polygons, and finally combining these parts into a complex geometric shape.
The prompt above was compiled from the original drawing commands and is for reference only.