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Deterministic Monte Carlo Estimation of π

Deterministic Monte Carlo Estimation of π
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2021-11-07 19:32
CircleProbability & StatisticsGeometric Construction
This example demonstrates the deterministic Monte Carlo method to estimate the value of π. Key mathematical concepts include probability and geometry. By constructing a circle and randomly placing points, the ratio of points inside the circle to the total number of points is calculated to estimate π. Commands used include Circle, Flatten, RemoveUndefined, and Length. Suitable for high school mathematics education and learning probability and statistics.

GeoGebra Commands & Parameters

  1. Circle(O, 1) → c
  2. Flatten(Sequence[Sequence[(i, j), i, 0, 1, 1 / n], j, 0, 1, 1 / n]) → l1
  3. RemoveUndefined(Sequence[If[(x(Element[l1, k]))^(2) + (y(Element[l1, k]))^(2) ≤ 1, Element[l1, k]], k, 1, Length[l1]]) → l2
  4. Length(l2) → d
  5. Length(l1) → e

AI Drawing Prompt Reference

Draw a circle with radius 1, then randomly generate a large number of points in the range of 0 to 1, count the number of points inside the circle and the total number of points, and estimate the value of π by the ratio of points inside the circle to the total number of points.
The prompt above was compiled from the original drawing commands and is for reference only.