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Geometric Relations of Squares and Cones

Geometric Relations of Squares and Cones
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2018-05-12 06:04
PolygonSolid GeometryCalculusGeometric Construction
In collections Homothety, Rotation Symmetry -RO
This example demonstrates the geometric relationships between squares, cones, and their circumcircles. Core math concepts include square construction, cone slant height, circumcircle, differential calculus, and means. Construction highlights involve GeoGebra commands: Polygon, Midpoint, Dilate, Rotate. Suitable for high school students and math enthusiasts exploring spatial geometry and differential concepts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Midpoint(A, C) → E
  3. Dilate(poly1, 5 / 6, E) → poly1'
  4. Rotate(poly1', (-(12°)), E) → poly1''
  5. Dilate(poly1'', 5 / 6, E) → poly1'''
  6. Rotate(poly1''', (-(12°)), E) → q1
  7. Dilate(q1, 5 / 6, E) → q1'
  8. Rotate(q1', (-(12°)), E) → q1''
  9. Dilate(q1'', 5 / 6, E) → q1'''
  10. Rotate(q1''', (-(13°)), E) → q2
  11. Dilate(q2, 5 / 6, E) → q2'
  12. Rotate(q2', (-(12°)), E) → q2''
  13. Dilate(q2'', 5 / 6, E) → q2'''
  14. Rotate(q2''', -12°, E) → q3
  15. Dilate(q3, 5 / 6, E) → q3'
  16. Rotate(q3', (-(12°)), E) → q3''
  17. Dilate(q3'', 5 / 6, E) → q3'''
  18. Rotate(q3''', (-(12°)), E) → q4
  19. Dilate(q4, 5 / 6, E) → q4'
  20. Rotate(q4', (-(12°)), E) → q4''
  21. Dilate(q4'', 5 / 6, E) → q4'''
  22. Rotate(q4''', (-(12°)), E) → q5
  23. Dilate(q5, 5 / 6, E) → q5'
  24. Rotate(q5', (-(12°)), E) → q5''
  25. Dilate(q5'', 5 / 6, E) → q5'''
  26. Rotate(q5''', (-(12°)), E) → q6
  27. Dilate(q6, 5 / 6, E) → q6'
  28. Rotate(q6', (-(12°)), E) → q6''
  29. Dilate(q6'', 5 / 6, E) → q6'''
  30. Rotate(q6''', (-(12°)), E) → q7
  31. Dilate(q7, 5 / 6, E) → q7'
  32. Rotate(q7', (-(12°)), E) → q7''