int-1 / Pi_Mathematica

H*

Вычисление числа P методом Монте-Карло

*L

ClearAll@ntmax, n, m, x, y, pn, resD;

ntmax = 1000000;

m = 0;

For@n = 1, n ≤ ntmax, n = n + 1, x = Random@D; y = Random@D; If@x x + y y ≤ 1, m = m + 1D;

If@n 10 »» n 100 »» n 1000 »» n 10000 »» n 100000 »» n ntmax,

pn = PaddedForm@n, 9D;

res = PaddedForm@N@4 m ê nD, 813, 12<D;

Print@"n=", pn, " res=", resDDD;

Print@" Exact value of Pi= ", PaddedForm@N@Pi, 17D, 813, 12<DD;

Exact value of Pi= 3.141592653590

? For

For@start, test, incr, bodyD executes start, then

repeatedly evaluates body and incr until test fails to give True. More…

? Random

Random@ D gives a uniformly distributed pseudorandom Real in the range

0 to 1. Random@type, rangeD gives a pseudorandom number of the specified type, lying in the specified range. Possible types are: Integer, Real and Complex. The default range is 0 to 1. You can give the range 8min, max< explicitly; a range specification of max is equivalent to 80, max<. More…

? If

If@condition, t, fD gives t if condition evaluates to True, and f if it evaluates to False. If@condition, t, f, uD gives u if condition evaluates to neither True nor False. More…

? PaddedForm

PaddedForm@expr, nD prints with all numbers in expr padded to leave room for a total of n digits. PaddedForm@expr, 8n, f<D prints with approximate real numbers having exactly f digits to the right of the decimal point. More…