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Probability of Points in an Incircle of an Equilateral Triangle

Probability of Points in an Incircle of an Equilateral Triangle
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2019-04-11 00:48
TriangleCircleProbability & StatisticsGeometric ConstructionSlider Animation
This example demonstrates the statistical characteristics of randomly distributed points within the incircle of an equilateral triangle. Key math concepts include Probability & Statistics, Geometric Distribution, Continuity, Arithmetic Operations, and Geometric Construction. It is constructed using GeoGebra commands like Polygon, Intersect, Circle, Sequence, and Sum. Suitable for high school and above, illustrating the integration of stochastic processes and geometric distributions.

GeoGebra Commands & Parameters

  1. Polygon((0, 1), Rotate[(0, 1), (2 * π / 3)], 3) → poly1
  2. Intersect(yAxis, poly1) → A, B
  3. Intersect(xAxis, yAxis) → C
  4. Circle(C, A) → c
  5. Sequence(RandomPointIn[poly1], w, 1, 100) → l1
  6. Sequence(IsInRegion[l1(w), c], w, 1, 100) → l2
  7. Sum(l2) → a