MathPlotAI Logo MathPlotAI

Bicycle Gears Proportion and Fractions Demo

Bicycle Gears Proportion and Fractions Demo
Loading the math board and drawing, please wait…
2013-05-25 15:58
VectorTrigonometryCoordinate GeometryGeometric Construction
In collections GeoGebra and 4D Frame: ideas collection
This example demonstrates the mathematical relationship between gear ratios and fractions using a bicycle gear system. It involves core concepts like proportions, fractions, similar triangles, and logic. The construction utilizes GeoGebra commands and objects such as Point, Angle, Segment, CircleSector, Circle, Polygon, Sequence, Vector, Mirror, PolyLine, CircumcircleArc, Translate, Intersect, and Element. It is suitable for middle school and above students studying the application of geometry and algebra, or for physics education on transmission systems.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 2.5 * zr]) → C'
  2. Angle(C, A, C') → ang
  3. Segment(F, E) → l
  4. Segment(A, C') → a
  5. CircleSector(A, F, Rotate[F, t1, A]) → c
  6. Circle(B, wr) → e
  7. Polygon(F + v / 5, F + h / 10, F - h / 10) → fth, b, f, g
  8. Polygon(E + v / 5, E + h / 10, E - h / 10) → bth, i, j, k
  9. Sequence(Rotate[fth, t1 + i * 2 * π / fthr, A], i, 1, fthr) → list3
  10. Sequence(Rotate[bth, t2 + i * 2 * π / bthr, B], i, 1, bthr) → list4
  11. Segment(Mirror[F, A], Mirror[E, B]) → m
  12. Vector(E, F) → clv
  13. Mirror(F, A) → F'
  14. CircleSector(B, E, Rotate[E, t2, B]) → d
  15. Mirror(E, B) → E'
  16. Vector(F', E') → clv2
  17. PolyLine(A, B, G, A, H, G) → n
  18. CircumcircleArc(H, H - 3 * v, I) → p
  19. Translate(e, Vector[B, I]) → e'
  20. Sequence(Segment[Rotate[D, t2 + i * 2 * π / ws, B], Rotate[E, t2 + i * 2 * π / ws, B]], i, 1, ws) → list1
  21. Sequence(Segment[I, Rotate[J, t2 + i * 2 * π / ws, I]], i, 1, ws) → list2
  22. Polygon(G + 0.3 * v + h, G + 0.7 * v + h, G + 0.2 * v - h) → poly1, q, r, s
  23. Circle(M, 5 * zr) → d_1
  24. Circle(K, 6 * zr) → c_1
  25. Intersect(c_1, d_1, 2) → L
  26. Polygon(C' + 0.5 * h + 0.25 * v, C' + 0.5 * h - 0.25 * v, C' - 0.5 * h - 0.25 * v, C' - 0.5 * h + 0.25 * v) → poly2, b_1, e_1, f_1, g_1
  27. PolyLine(K, L, M) → a_1
  28. Mirror(C', A) → C''
  29. Mirror(poly2, A) → poly2'
  30. Circle(N, 5 * zr) → h_1
  31. Intersect(c_1, h_1, 2) → O
  32. PolyLine(K, O, N) → i_1
  33. Segment(A, C'') → j_1
  34. Circle(A, r1) → k_1
  35. Circle(B, r2) → p_1
  36. Sequence(Arc[k_1, Rotate[F, Min[3.141592653589793, Max[0, (clink * i + posModl) / cl1 * π]], A], Rotate[F, Max[0, Min[3.141592653589793, (clink * i + posModl + clink / 2) / cl1 * π]], A]], i, 0, round(cl1 / clink)) → list5
  37. Sequence(Arc[p_1, Rotate[E', Min[3.141592653589793, Max[0, (clink * i + posModr) / cl2 * π]], B], Rotate[E', Max[0, Min[3.141592653589793, (clink * i + posModr + clink / 2) / cl2 * π]], B]], i, 0, round(cl2 / clink)) → list7
  38. Sequence(Segment[F' + clv2 * Min[1, Max[0, (clink * i + posModb) / l]], F' + clv2 * Min[1, Max[0, (clink * i + posModb + clink / 2) / l]]], i, 0, If[clink * nclink + posModb > l, nclink - 1, nclink]) → list6
  39. Sequence(Segment[E + clv * Min[1, Max[0, (clink * i + posModt) / l]], E + clv * Min[1, Max[0, (clink * i + posModt + clink / 2) / l]]], i, 0, If[clink * nclink + posModb > l, nclink - 1, nclink]) → list8
  40. Element(list1, Length[list1]) → l_1

AI Drawing Prompt Reference

Draw a bicycle gear system to demonstrate the relationship between gear ratios and fractions. Include two gears, represented by points for axles and sectors for the gears themselves. Use polygons to depict the teeth of the gears. Illustrate the direction of transmission between gears with vectors and the outlines with circles. Connect the teeth with arcs and show the tooth shapes with polygons. Link the axles with line segments and represent the rotation with arcs. Use vectors to indicate the rotation direction and polygons for the rotation paths.
The prompt above was compiled from the original drawing commands and is for reference only.