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Can Random Cuts Form a Triangle?

Can Random Cuts Form a Triangle?
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2015-12-07 06:22
TriangleProbability & StatisticsGeometric Construction
This example demonstrates how to form a triangle by randomly cutting a piece of spaghetti. Key math concepts include geometric construction and probability & statistics. It uses commands like If, Corner, Polygon, Segment, RotateText. Suitable for middle school and above students to learn geometric construction and probability & statistics.

GeoGebra Commands & Parameters

  1. If(t < 4, 0.5 - ((x - 0.5) * Min[1, Max[0, t - 2]]), ((1 - ((1 - x) * Min[1, Max[0, 5 - t]])) * (1 - x) / x)) → h
  2. Corner(1, 5) → A
  3. Polygon((0, 0), (1, 0), 4) → poly1
  4. Segment((0, 0), (1, 1)) → a
  5. RotateText("location of cuts along stick", 90°) → text1
  6. RotateText("first cut", 45°) → text3
  7. IntegralBetween(m, h, 0.5, 1) → RightGreen
  8. RotateText("probability of triangle", 90°) → text5
  9. If(t < 4, 0.5 + (x * (1 + Min[1, Max[0, t - 2]])) - (0.5 * Min[1, Max[0, t - 2]]), ((1 - (x * Min[1, Max[0, 5 - t]])) * x / (1 - x)) + (x * Min[1, Max[0, 5 - t]])) → g
  10. IntegralBetween(f, g, 0, 0.5) → LeftGreen

AI Drawing Prompt Reference

Draw a line segment from left to right with a length of 1. Randomly select two points on the line to cut it into three parts. Calculate and display the probability that these three parts can form a triangle. Draw a green area to represent the probability of forming a triangle.
The prompt above was compiled from the original drawing commands and is for reference only.