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Geometric Construction of Toyota Logo

Geometric Construction of Toyota Logo
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2019-11-27 20:28
CirclePolygonVectorTrigonometryGeometric Construction
This example demonstrates how to construct the geometric shapes of the Toyota logo using GeoGebra. It involves core mathematical concepts such as angles, circles, geometry, line segments, linear regression, differential calculus, conic sections, logarithms, plane figures, vectors, orthogonal lines, orthogonal vectors, intersections, polygons, centroids, mirroring, ellipses, midpoints, circle arcs, and line segments. Key construction steps include using commands like LineBisector, Vector, OrthogonalLine, OrthogonalVector, Intersect, Polygon, Centroid, Mirror, Ellipse, Midpoint, CircleArc, and Segment. Suitable for high school mathematics education or for enthusiasts of geometric constructions.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → j
  2. Vector(A, B) → u
  3. OrthogonalLine(B, u, xOyPlane) → g
  4. OrthogonalVector(u) → v
  5. OrthogonalLine(C, v, xOyPlane) → f
  6. Intersect(g, f) → D
  7. LineBisector(C, A) → i
  8. Polygon(A, B, D, C) → c1, a, b, d, c
  9. Centroid(c1) → H
  10. Mirror(K, j) → K'
  11. Ellipse(K', K, E, xOyPlane) → e
  12. Mirror(G, i) → G'
  13. Mirror(I, j) → I'
  14. Ellipse(I, I', G, xOyPlane) → h
  15. Midpoint(C, A) → J
  16. LineBisector(E, H, xOyPlane) → k
  17. Intersect(j, k) → L
  18. Mirror(M, j) → M'
  19. Ellipse(M', M, E, xOyPlane) → p
  20. Mirror(N, j) → N'
  21. Ellipse(N', N, G, xOyPlane) → q
  22. Mirror(O, i) → O'
  23. Ellipse(O, O', G, xOyPlane) → r
  24. Mirror(P, i) → P'
  25. Ellipse(P, P', Q, xOyPlane) → s
  26. Mirror(Q, j) → Q'
  27. Intersect(p, s) → R, S, ,
  28. Intersect(s, q) → T, U, ,
  29. Polygon(T, R, S, U) → c2, t, r_1, s_1, u_1
  30. CircleArc(V, R, S, xOyPlane) → c_1
  31. Segment(T, U) → l
  32. LineBisector(T, R, xOyPlane) → m
  33. Intersect(j, m) → Z
  34. CircleArc(Z, T, R, xOyPlane) → e_1
  35. Mirror(e_1, j) → f_1
  36. Segment(T, R) → n
  37. Mirror(T, j) → T'
  38. Mirror(R, j) → R'
  39. Segment(T', R') → n'
  40. CircleArc(W, T, Q', xOyPlane) → d_1
  41. Segment(T, U) → g_1
  42. Segment(R, S) → h_1

AI Drawing Prompt Reference

Draw a geometric design resembling the Toyota logo, incorporating interconnected circles, polygons, and ellipses. Start by constructing a quadrilateral, find its centroid, and draw an ellipse centered at this point. Then, create multiple symmetric ellipses and circular arcs using mirroring and rotation, and finally connect key points with line segments to form the logo's outline.
The prompt above was compiled from the original drawing commands and is for reference only.