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Mathematical Modeling of the Apple Logo

Mathematical Modeling of the Apple Logo
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2021-12-26 00:27
CircleFunctionOptimizationGeometric Construction
This example demonstrates the geometric construction of the Apple logo using mathematical tools; core concepts include circles, symmetry, quadratic functions, and coordinate geometry; construction highlights from the summary involve commands like Point, Circle, Center, Mirror, and CircumcircleArc in GeoGebra; suitable for high school and above learners to understand geometric constructions and function applications.

GeoGebra Commands & Parameters

  1. Point(j) → D
  2. Circle(D, C, E) → c
  3. Center(c) → F
  4. Mirror(F, yAxis) → F'
  5. Circle(F', Segment[D, F]) → d
  6. Point(d) → G
  7. Circle(K, M, J) → k
  8. Circle(G, H, I) → g
  9. Center(g) → N
  10. CircumcircleArc(G, H, I) → h
  11. Point(d) → O
  12. Point(j) → P
  13. CircumcircleArc(G, O, P) → p
  14. CircumcircleArc(D, C, E) → r
  15. Circle(E, R, Q) → c_1
  16. Center(c_1) → S
  17. CircumcircleArc(E, R, Q) → d_1
  18. CircumcircleArc(K, L, J) → e_1
  19. Center(k) → U
  20. CircumcircleArc(K, M, J) → f_1
  21. Point(e_1) → T
  22. Circle(K, L, T) → e

AI Drawing Prompt Reference

Draw the Apple logo by first creating a circle, then drawing a line of symmetry through its center. Next, draw a circle with a point on the symmetry line as its center. Then, draw another circle using the intersection points of the previous circles to form part of the logo. Finally, use specific points to draw arcs to complete the logo.
The prompt above was compiled from the original drawing commands and is for reference only.