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Italian Pasta: Spiral Tubes

Italian Pasta: Spiral Tubes
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2015-07-28 01:17
FunctionCoordinate GeometryGraphing
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This example demonstrates a shape of Italian pasta - spiral tubes. It involves the concept of functions, particularly using the Surface and Polygon commands to construct the spiral tubes. By adjusting parameters, you can observe the changes in the spiral tubes. Suitable for high school mathematics education, especially for teaching coordinate geometry and function graphs.

GeoGebra Commands & Parameters

  1. If(d ≟ 0 ∨ d ≟ 36, 4, If[d ≟ 9 ∧ b ≟ 4 ∨ d ≟ 27 ∧ b ≟ (-4), 5, If[(0 < d) ∧ (d < 9) ∨ (27 < d) ∧ (d < 36), 3, If[d ≟ 18, 2, If[(9 < d) ∧ (d < 18) ∨ (18 < d) ∧ (d < 27), 1, 0]]]]) → sf
  2. If(Mod[c, 3.141592653589793] ≟ π / 4, true, false) → w0
  3. Surface((scl * ((8 * cos(((1 / 70 * π) * k))) + (0.2 * cos(((2 / 7 * π) * k))) + (5 * cos(((0.01 * π) * j))))), (scl * ((8 * sin(((1 / 70 * π) * k))) + (0.2 * sin(((2 / 7 * π) * k))) + (4 * sin(((0.01 * π) * j))))), ((scl * 1.2) * j), k, 0, 140, j, 0, 50) → f_2
  4. Polygon(C, D, E, F) → Vieleck1, c_1, d_1, e, f

AI Drawing Prompt Reference

Draw a spiral tube resembling Italian pasta, generated by function graphs showing shape changes with parameter adjustments, featuring segmented surfaces and connected polygonal faces, creating a continuous ascending spiral effect suitable for teaching function and coordinate geometry.
The prompt above was compiled from the original drawing commands and is for reference only.