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Cutting The Winding Strip

Cutting The Winding Strip
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2014-01-31 19:15
FunctionTrigonometryCoordinate GeometryOptimizationGeometric Construction
This example demonstrates how to cut a magnetic strip wound around a circular roll into equal-length pieces without unwinding it. It involves math concepts like distributions, congruence, multiplication, dilation, polygons, and Pythagorean theorem. Construction uses commands/objects such as Circle, Sequence, Textfield, CurveCartesian. Suitable for high school and above, illustrating the integration of geometric construction and algebraic computation.

GeoGebra Commands & Parameters

  1. Circle((0, 0), r) → c
  2. Sequence(CurveCartesian[((r + (k * t)) * cos(s)), ((r + (k * t)) * sin(s)), s, 0, maxs], k, 0, maxk) → rulle1
  3. Sequence(CurveCartesian[((r + (k * t)) * cos(maxs)) - (s * sin(maxs)), ((r + (k * t)) * sin(maxs)) + (s * cos(maxs)), s, 0, ((-r) * tan(maxs))], k, 0, maxk) → rulle2
  4. Sequence(CurveCartesian[r + t + ((k * t) * cos(s)), ((k * t) * sin(s)), s, maxs, 6.28319], k, 0, maxk) → rulle3
  5. Textfield(t) → tekstfelt1
  6. Textfield(r) → tekstfelt2
  7. Textfield(maxk) → tekstfelt3
  8. Sequence(Mod[((-maxs) * ((k * r) + ((k * (k + 1) / 2) * t))) - ((k - 1) * straight) - (((k - 1) * k / 2) * curved), d], k, 1, maxk) → mods
  9. Textfield(d) → tekstfelt4
  10. CurveCartesian(cos(s), sin(s), s, 0, 6.283185307179586) → e
  11. Sequence(Mod[((-maxs) * (((k - 1) * r) + (((k - 1) * k / 2) * t))) - ((k - 1) * straight) - (((k - 1) * k / 2) * curved), d], k, 1, maxk) → mods3
  12. Sequence(Sequence[((r + (k * t)) * e(s)), s, Element[mods3, k] / (r + (k * t)), maxs, d / (r + (k * t))], k, 1, maxk) → cuts
  13. Sequence(Mod[((-maxs) * ((k * r) + ((k * (k + 1) / 2) * t))) - (k * straight) - (((k - 1) * k / 2) * curved), d], k, 1, maxk) → mods2
  14. Sequence(Sequence[((r + (k * t)) * e(maxs)) + (s * e(maxs + π / 2)), s, Element[mods, k], straight, d], k, 1, maxk) → cuts2
  15. Sequence(Sequence[(r + t, 0) + ((k * t) * e(s)), s, maxs + Element[mods2, k] / ((k * t)), 6.283185307179586, d / ((k * t))], k, 1, maxk) → cuts3

AI Drawing Prompt Reference

Draw a circular roll with a magnetic strip wound around it, demonstrating how to cut the strip into equal-length pieces without unwinding. Incorporate mathematical concepts like distributions, congruence, multiplication, dilation, polygons, and Pythagorean theorem. Start by drawing the circular roll, then depict the magnetic strip wound around it, followed by calculating and plotting the cutting lines, and finally label key parameters such as radius, maximum number of turns, and cut lengths.
The prompt above was compiled from the original drawing commands and is for reference only.