用投针法估算圆周率

GeoGebra 命令及参数

1. Polygon(A, B, C, D) → veelhoek1, a, b, c, d
2. Point(d) → E
3. Point(b) → F
4. Segment(E, F) → e
5. Segment(A, B) → f
6. Segment(C, B) → g
7. Point(d) → G
8. Point(b) → H
9. Segment(G, H) → h
10. Point(d) → I
11. Point(b) → J
12. Segment(I, J) → i
13. Point(d) → K
14. Sequence((RandomUniform[-2.5, 3.5], RandomUniform[-0.5, 4]), i, 1, n) → P1vec
15. Sequence(RandomUniform[0, (2 * pi)], i, 1, n) → tvec, {4.224314739236119, 0.1620309745740437, 0.4605174958970105, 5.8280675830396165, 0.744161317665743, 1.8950184671540102, 1.7448102507675507, 5.309910014879022, 6.121364058267303, 2.85233922296365, 4.5432563379663575, 1.9293444101147605, 0.2209098581627405, 4.760290833211964, 4.392725641912982, 3.7223023181218, 0.6833766698023622, 4.479767534124977, 3.0869341129502894, 4.3306704252319514, 1.8141970573153536, 4.658387995302705, 4.060088957673371, 6.063079435544543, 2.061083837096798, 2.300831404182145, 1.8272273818602187, 6.254394191111447, 1.458612536728336, 0.15412415171460267, 2.2985130436859187, 3.261072983316622, 2.301454092739077, 1.9204124547620725, 2.0132456547024944, 1.7121227995302601, 5.178665063775763, 3.710385445469193, 1.8039787409911392, 1.7956809440909547, 3.4049735494995033, 4.906787019889882, 0.031184358684351324, 0.41703356988646634, 4.122052548459889, 0.303443722740441, 4.979164698615041, 6.2009597525578934, 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16. Sequence((x(Element[P1vec, i]) + (1.5 * cos(Element[tvec, i])), y(Element[P1vec, i]) + (1.5 * sin(Element[tvec, i]))), i, 1, n) → P2vec
17. Sequence(If[floor(((y(Element[P1vec, i]) + 2) * 2 / 3)) ≟ floor(((y(Element[P2vec, i]) + 2) * 2 / 3)), 0, 1], i, 1, n) → telvec
18. Sum(telvec) → teller
19. Sequence(Segment[Element[P1vec, i], Element[P2vec, i]], i, 1, n) → naald
20. Intersect(d, a) → O
21. Point(d) → P
22. Segment(O, P) → j
23. Intersect(c, b) → Q
24. Segment(P, Q) → k
25. Point(d) → R
26. Segment(R, S) → l
27. Sequence(Element[naald, i], i, 1, m) → naaldm
28. Sequence(Element[telvec, i], i, 1, m) → telvecm
29. Sum(telvecm) → total
30. If(total ≟ 0, 0, (2 * m / total)) → prob2
31. If(total ≟ 0, 0, (2 * m / total)) → prob