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Dynamic Geometric Constructions

Dynamic Geometric Constructions
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2017-02-26 21:19
PolygonVectorTrigonometryInequalityGeometric Construction
This example demonstrates dynamic geometric constructions involving polygons, rotations, and vector operations to illustrate concepts like geometric constructions, inequalities, and trigonometric functions. Key GeoGebra commands used include Polygon, Rotate, If, and Vector. Suitable for high school mathematics education or exploration by geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E, F, G, H, I, J) → poly1, a, j, b, c, d, e, f, g, h, i
  2. Rotate(A, 90°, K) → A'
  3. Rotate(B, 90°, K) → B'
  4. Rotate(C, 90°, K) → C'
  5. Rotate(D, 90°, K) → D'
  6. Rotate(E, 90°, K) → E'
  7. Rotate(F, 90°, K) → F'
  8. Rotate(G, 90°, K) → G'
  9. Rotate(H, 90°, K) → H'
  10. Rotate(I, 90°, K) → I'
  11. Rotate(J, 90°, K) → J'
  12. Polygon(A', B', C', D', E', F', G', H', I', J') → poly1', a', j', b', c', d', e', f', g', h', i'
  13. If(1 ≤ k < 2, Dilate[B, 2 - k, B'], Dilate[B, 0, B']) → M
  14. Vector(B, M) → u

AI Drawing Prompt Reference

Draw a dynamic polygon formed by nine points, rotate each point by 90 degrees nine times, and mark the rotated points. Reconstruct a new polygon using these rotated points. Then, based on the value of a variable k, scale point B, with a scaling factor of 2-k if k is between 1 and 2, or 0 otherwise. Finally, connect point B to the scaled point M and draw vector u.
The prompt above was compiled from the original drawing commands and is for reference only.