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Counters for LZ 2: Cosine Multiplication Sequence on a Cylinder

Counters for LZ 2: Cosine Multiplication Sequence on a Cylinder
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2017-06-21 06:16
CircleTrigonometrySequenceSolid GeometrySlider Animation
In collections Virtual Manipulatives
This GeoGebra example constructs a set of counter objects named 'Counters for LZ 2' to demonstrate the combination of cosine functions and multiplication sequences on a cylindrical surface. The core mathematical concepts involve cosine, sequences and series, multiplication, and the parametric representation of a cylinder. The construction uses the Circle command to create multiple circles as the basis for counters, generating objects counter01 through counter25, along with control points A, B, C, etc., and a reset button for dynamic counting and sequence display. This example is suitable for high school or college-level teaching of trigonometry, sequences, and solid geometry, and can be used to visualize periodic phenomena on curved surfaces.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → chip25
  2. Circle(A_1, 1) → chip24
  3. Circle(B, 1) → chip12
  4. Circle(C, 1) → chip08
  5. Circle(D, 1) → chip11
  6. Circle(E, 1) → chip02
  7. Circle(F, 1) → chip09
  8. Circle(G, 1) → chip03
  9. Circle(H, 1) → chip01
  10. Circle(I, 1) → chip07
  11. Circle(J, 1) → chip20
  12. Circle(K, 1) → chip17
  13. Circle(L, 1) → chip21
  14. Circle(M, 1) → chip22
  15. Circle(N, 1) → chip23
  16. Circle(O, 1) → chip06
  17. Circle(P, 1) → chip18
  18. Circle(Q, 1) → chip10
  19. Circle(R, 1) → chip15
  20. Circle(S, 1) → chip13
  21. Circle(T, 1) → chip19
  22. Circle(U, 1) → chip14
  23. Circle(V, 1) → chip16
  24. Circle(W, 1) → chip04
  25. Circle(Z, 1) → chip05

AI Drawing Prompt Reference

Draw a set of 25 equal-radius circles on a cylindrical surface, each centered at distinct points along the curved surface, all with radius 1. Arrange them in a spiral or grid-like pattern without overlapping, representing a cosine multiplication sequence. Include a slider to dynamically adjust the sequence or phase, and a reset button. The circles symbolize discrete samples of periodic phenomena on the curved surface, illustrating the geometric relationship between trigonometric functions and sequences.
The prompt above was compiled from the original drawing commands and is for reference only.