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Geometric Construction of sqrt(3)

Geometric Construction of sqrt(3)
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2018-02-23 04:03
CircleCoordinate GeometryGeometric Construction
This example demonstrates how to geometrically construct the length of sqrt(3) using GeoGebra commands like Point, Segment, Circle, Intersect, Line, Semicircle, Distance, OrthogonalLine, and Midpoint. It involves core concepts in coordinate geometry, properties of circles, and orthogonal lines. Suitable for high school mathematics education and geometric construction learning.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 3]) → B
  2. Segment(A, B) → f
  3. Point(Circle[B, 1]) → C
  4. Segment(B, C) → g
  5. Point(f) → D
  6. Circle(C, D) → c
  7. Circle(A, Segment[C, D]) → d
  8. Intersect(c, d) → E, F, ,
  9. Line(F, E) → h
  10. Intersect(f, h) → G
  11. Point(f) → H
  12. Circle(C, H) → e
  13. Point(g) → I
  14. Circle(G, I) → k
  15. Intersect(e, k, 2) → J
  16. Intersect(e, k, 1) → K
  17. Line(J, K) → i
  18. Semicircle(A, C) → p
  19. Intersect(p, i, 1) → L
  20. Distance(L, B) → distanceLB
  21. Distance(A, B) → distanceAB
  22. OrthogonalLine(B, f) → j
  23. Point(p) → M
  24. OrthogonalLine(M, f) → l
  25. Distance(M, B) → distanceMB
  26. Midpoint(M, B) →
  27. Intersect(l, f) → N
  28. Distance(M, L) → distanceML
  29. Midpoint(M, L) →
  30. Distance(M, N) → distanceMN
  31. Midpoint(M, N) →