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Geometric Construction of the Microsoft Logo

Geometric Construction of the Microsoft Logo
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2020-03-30 05:08
PolygonVectorSolid GeometryTransformationGeometric Construction
This GeoGebra example reconstructs the Microsoft logo using precise geometric construction, demonstrating how basic geometric elements and transformation commands can build an iconic design. The core mathematical concepts involve quadrilaterals, rectangles, ellipses, multiplication, solids or 3D shapes, and rotation. The construction uses commands such as Line, OrthogonalLine, Vector, OrthogonalVector, LineBisector, Intersect, Mirror, and Polygon, along with numerous auxiliary objects (points, lines, circles, text, and images) to support the process. This example is suitable for middle school to university-level geometry instruction, helping students understand geometric transformations, symmetry, and the application of mathematical tools in real-world design, while also enhancing spatial reasoning and construction skills.

GeoGebra Commands & Parameters

  1. Line(A, B) → s
  2. OrthogonalLine(A, s) → b
  3. Vector(A, B) → u
  4. OrthogonalVector(u) → v
  5. OrthogonalLine(F, b) → f
  6. OrthogonalLine(A_1, b) → r
  7. LineBisector(A, B) → m
  8. Intersect(m, f) → E
  9. Mirror(H, m) → H'
  10. OrthogonalLine(H', s) → k
  11. OrthogonalLine(B, u, xOyPlane) → g
  12. Intersect(g, r) → C
  13. Polygon(A_1, C, B, A) → q1, a_1, c, b_1, a_2
  14. LineBisector(A_1, A) → h
  15. Mirror(f, h) → f'
  16. OrthogonalLine(D, s) → i
  17. Intersect(k, f') → K
  18. Mirror(k, m) → k'
  19. Mirror(i, m) → i'
  20. Intersect(h, b) → G
  21. Line(I, h) → j
  22. Mirror(j, h) → j'
  23. Intersect(i, f') → J
  24. Intersect(i, j) → L
  25. Intersect(j, k) → M
  26. Polygon(L, M, K, J) → q2, l, m_1, k_1, j_1
  27. Mirror(L, m) → L'
  28. Mirror(M, m) → M'
  29. Mirror(K, m) → K'
  30. Mirror(J, m) → J'
  31. Polygon(L', M', K', J') → q2', l', m', n, p
  32. Mirror(L, h) → L'_1
  33. Mirror(M, h) → M'_1
  34. Mirror(K, h) → K'_1
  35. Mirror(J, h) → J'_1
  36. Polygon(L'_1, M'_1, K'_1, J'_1) → q2'_1, l'_1, m'_1, k'_1, j'_1
  37. Mirror(L', h) → L''
  38. Mirror(M', h) → M''
  39. Mirror(K', h) → K''
  40. Mirror(J', h) → J''
  41. Polygon(L'', M'', K'', J'') → q2'', l'', m'', k'', j''

AI Drawing Prompt Reference

Draw a square grid composed of four identical rectangles, each containing a smaller square inside, forming a symmetric pattern resembling the Microsoft logo. Start with a horizontal baseline and a vertical line intersecting at the center. Construct two adjacent rectangles based on these lines, then use mirroring and rotation to replicate the rectangle group into all four quadrants. Inside each rectangle, outline a smaller square with thin lines to create a nested effect. The final figure is a symmetric, orderly geometric composition with lines, perpendiculars, angle bisectors, intersection points, polygons, and mirror transformations.
The prompt above was compiled from the original drawing commands and is for reference only.