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. , ζ, , E (ζ) . ζ, .

1. . G, b. , . , G , G, . π, , , 100000 . .

 

154. π -

Program Chislo_Pi;

Uses Crt; Var I, N: Longint; X, Y: Real;

Begin

Randomize; N:= 0;

For I:= 1 To 100000 Do

Begin

X := Random; Y:= Random;

If Sqr(X - 0.5) + Sqr(Y - 0.5) < 0.25 Then N:= N + 1

End;

WriteLn ('pi=', (N / 100000 / Sqr(0.5)): 8: 5);

Repeat Until KeyPressed End.

 

2. . , , L, l (. 7.60). , , , ?

. 7.60. .

 

. (XVIII .) : = . , L = 2 l, = . , = , N - , N1 - .

, = . π.

. L = 1 l = . , , 2020, (0, 0). , 0 20. , , ; , , - - . ;

(1, y1), B(x2, 2);

1(1 + α(2 1), 1 + α(2 1)),

, , , , - , oe A 1 .

 

155 .

Program Buffon;

Uses Crt; Var I, J, K, M, N: Integer; XI, X2, Y1, Y2, Al: Real;

Begin

Randomize; M:= 30000; N:= 1;

For I:= 1 To M Do

Begin

X1:= Random * 20; Yl:= Random * 20; X2:= Random * 20;

Y2:= Random * 20;

A1:= 0.5 / Sqrt(Sqr(X2 X1) + Sqr(Y2 - Yl));

J:= Round(Yl); := Round(Yl + A1 * (Y2 Y1));

If J <> Then N:= H + 1

End;

WriteLn('pi=', W / N): 8: 5); Repeat Until KeyPressed

End.

 

, , .

. , , , -, . . ? , ? , , . ? , , , ( ), .

3. . , G . , .. , U . ) , . U(r) = 0; U(r) - , ; , , .

. 7.61.

 

G . , , , U . U(A) A (. 7.61).

, , . , . . , f (i) , , N . ,

, .

4. ( ). () : [0, 1] 0,5, x = + h, x = - h.

 

156.

Program Tochka;

Uses Crt, Graph; Var I, J: Integer; Z, P, X, H, Y: Integer;

Begin

X:= 320; Y:= 240; H:= 10; P:= 4; DetectGraph(I, J);

InitGraphd, J, ");

SetColor(15); Line(10, 312, 630, 312); Randomize;

Repeat

Z:= Random(8); If Z >= P Then X:= X + H Else X:= X - H;

SetColor(Green); Circle(X, Y, 10); Delay(200);

SetColor(0); Circle(X, Y, 10)

Until KeyPressed Or (X >= 640) Or (X <= 0); CloseGraph

End.

 

, , [0, hmax] . H:= Random(HMax).

, - (0 < < 1, 0 < y < 1), . () .

 

157.

Program Broun;

Uses Crt, Graph;

Var I, J, X, Y, HxMax, HyMax, Hx, : Integer; PI, P2, Z1, Z2: Real;

Begin

X:= 320; Y:== 240; HxMax:= 30; PI:= 0.5; P2:= 0.5; HyMax:= 30;

DetectGraph (I, J); InitGraph (1, J, ''); SetColor(15);

Randomize; RectAngle(100, 100, 540, 380);

SetColor(Green); Circle(X, Y, 10); Delay(200); SetColor(0);

Circle(X, , 10);

Repeat

Zl:= Random; Z2:= Random; Hx:= Random(HxMax);

:= Random(HyMax);

If (Zl < PI) Then X:= X + Hx Else X:= X - Hx;

If (Z2 < P2) Then Y:= Y + Else Y:" - ;

If X <= 110 Then X:= X + 2 * (110 - X);

If X >= 530 Then X:= X - 2 * (-530 + X);

If Y <= 110 Then Y:= Y + 2 * (110 - Y);

If Y >= 370 Then Y:= Y - 2 * (Y - 370);

SetColor(Green); Circle(X, Y, 10); Delay(100);

SetColor(0); Circle(X, Y, 10)

Until Keypressed; CloseGraph

End.

 

( ) , . , . . .

 

158.

Program Gaz;

Uses Crt, Graph;

Var I, J, HxMax, HyMax, Hx, , N, I: Integer;

X, Y: Array[0..500] Of Integer; PI, P2, Z1, Z2: Real;

Begin N:= 100;

For I:= 1 To N Do Begin X[I]:= 320; Y[I]:= 240 End;

HxMax:= 10; PI:= 0.5; P2:= 0.5; HyMax:= 10;

DetectGraph (1, J); InitGraphd, J, ' '); SetColor(15);

Randomize; RectAngle(100, 100, 540, 380);

For I:= 1 To N Do PutPixel(X[I], Y[I], White); Delay(200);

For I:= 1 To N Do PutPixel(X(I], Y[I], 0);

Repeat

For I:= 1 To N Do

Begin

Zl:= Random; Z2:= Random;

Hx:= Random(HxMax); := Random(HyMax);

If Zl < PI Then X[I]:= X[I] + Hx Else X[I]:= X[I] Hx;

If Z2 < P2 Then Y[I]:= Y[I] + Else Y[I]:= Y[I] - ;

If X[I] <= 110 Then X[I]:= X[I] + 2 * (110 - X[I]);

If X(I] >= 530 Then X[I]:= X[I] - 2 * (-530 + [I];

If Y[I] <= 110 Then Y(I]:= Y[I] + 2 * (110 - Y[I]);

If Y[I] >= 370 Then Y[I]:= Y[I] - 2 * (Y[I] - 370);

PutPixel (X[I], Y[I], 15)

End; Delay(100);

For I:= 1 To N Do PutPixel(X[I], Y[I], 0)

Until KeyPressed; CloseGraph

End.

 

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18. () ? ?

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24. , : ) ; ) ; ) .

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