{$N+}
Program CalcPI(input, output);
{ Not the most efficient Program I've ever written. Mostly it's quick and
dirty. The infinite series is very effective converging very quickly.
It's much better than Pi/4 = 1 - 1/3 + 1/5 - 1/7 ... which converges
like molasses. }
{ Pi / 4 = 4 * (1/5 - 1/(3*5^3) + 1/(5*5^5) - 1/(7*5^7) + ...) -
(1/239 - 1/(3*239^3) + 1/(5*239^5) - 1/(7*239^7) + ...) }
{* Infinite series courtesy of Machin (1680 - 1752). I found it in my
copy of Mathematics and the Imagination by Edward Kasner and
James R. Newman (Simon and Schuster, New York 1940, p. 77) * }
Uses
Crt;
Var
Pi_Fourths,
Pi : Double;
Temp : Double;
ct : Integer;
num : Integer;
Function Power(Number, Exponent : Integer) : double;
Var
ct : Integer;
temp : double;
begin
temp := 1.00;
For ct := 1 to Exponent DO
temp := temp * number;
Power := temp
end;
begin
ClrScr;
ct := 1;
num := 1;
Pi_Fourths := 0;
While ct < 15 DO
begin
Temp := (1.0 / (Power(5, num) * num)) * 4;
if ct MOD 2 = 1 then
Pi_Fourths := Pi_Fourths + Temp
ELSE
Pi_Fourths := Pi_Fourths - Temp;
Temp := 1.0 / (Power(239, num) * num);
if ct MOD 2 = 1 then
Pi_Fourths := Pi_Fourths - Temp
ELSE
Pi_Fourths := Pi_Fourths + Temp;
ct := ct + 1;
num := num + 2;
end;
Pi := Pi_Fourths * 4.0;
Writeln( 'PI = ', Pi);
end.