MathPlotAI Logo MathPlotAI

Logo BQ: Geometric Construction with Transformations and Conics

Logo BQ: Geometric Construction with Transformations and Conics
Loading the math board and drawing, please wait…
2019-07-11 05:26
CircleVectorTransformationGeometric Construction
① This GeoGebra example constructs a geometric logo named 'Logo BQ', combining lines, perpendiculars, perpendicular bisectors, vectors, midpoints, intersections, reflections, ellipses, polygons, and circles to form a symmetric emblem. ② Core mathematical concepts include 2D vectors, angles, circles and ellipses, quadratic functions, derivatives, translations, and geometric transformations (reflection/symmetry), blending analytic geometry and transformation geometry. ③ Construction highlights: from the summary, commands such as Line, OrthogonalLine, LineBisector, Vector, OrthogonalVector, Midpoint, Intersect, Mirror, Ellipse, Polygon, and Circle are used, with numerous objects (A, B, f, g, h, i, u, v, C, D, E, j, G, F, F', c, d, H, I, J, K, L, q1, k, l, etc.) created and mirrored to complete the logo. ④ Suitable for high school or early college students to learn geometric construction, vectors, and transformations, and as a creative design example linking mathematics with art.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. OrthogonalLine(B, f) → h
  4. LineBisector(A, B) → i
  5. Vector(A, B) → u
  6. OrthogonalVector(u) → v
  7. Midpoint(A, B) → C
  8. LineBisector(A, D) → j
  9. Intersect(j, f) → G
  10. Mirror(F, f) → F'
  11. Ellipse(F, F', A) → c
  12. Ellipse(F, F', E) → d
  13. Polygon(K, L, J, I) → q1, k, l, j_1, i_1
  14. Mirror(K, C) → K'
  15. Mirror(L, C) → L'
  16. Mirror(J, C) → J'
  17. Mirror(I, C) → I'
  18. Polygon(K', L', J', I') → q1', k', l', j', i'
  19. Mirror(c, C) → c'
  20. Mirror(d_6, C) → e
  21. Mirror(d, C) → d'
  22. Line(M, f) → m
  23. Intersect(h, m) → N
  24. Circle(O, N) → p
  25. OrthogonalLine(P, g) → n
  26. Intersect(i, n) → Q
  27. Circle(Q, R) → q
  28. Circle(S, T) → r
  29. Mirror(Q, g) → Q'
  30. Mirror(q, g) → q'
  31. Mirror(h, g) → h'
  32. Intersect(h', f) → U
  33. Circle(V, W) → s

AI Drawing Prompt Reference

Draw a geometric logo with two lines f and g, which are perpendicular to points A and B. Then find the midpoint C of line segment AB and draw a perpendicular line j through C. Line j intersects line f at point G. Use points F and F' to construct ellipses c and d, where F' is the reflection of F across line f. Draw quadrilateral KLIJ and its reflection K'L'J'I'. Then reflect points F and F' across point C to get c' and d'. Draw line m through point M and line f, which intersects line h at point N, and then draw a circle p with radius N. Draw points Q and R, and circles q and r with radii Q and R, then reflect them to get Q' and q'. Finally, find the intersection point U of line h' and line f, and draw a circle s with radius U.
The prompt above was compiled from the original drawing commands and is for reference only.