Estimating π with random points and strips
Count random points in a quarter circle to estimate π, see how the scatter shrinks with more points, and compare with the strip method.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- France: grade 7
- Germany: grade 10
- Syria: grade 6
- Palestine: grade 6
- Ukraine: grade 6
Guide
A quarter circle of radius 1 has the area π/4 and lies in the unit square of area 1. If points fall at random into the square, the share k/n of points inside the quarter circle is about π/4.
A point P(x|y) is inside when x2 + y2 ≤ 1. In a spreadsheet you check this with an IF condition. Then π ≈ 4·kn.
Each run gives a different value. With more points the values scatter less around the true value.
The strip method does not use chance: you add the areas of rectangles under the quarter circle and multiply by 4.