Math Question!

[TViYH]

Ok. I made a function that uses Sqrt, and a few others. The question is, how, when using other numbers, multiplication, division, and addition, does it come out to be the same result?

Example:

Successfully compiled (61 ms)
Original number : 81
Number after Result := (((Result + Result) + 5) / 2) - 2.5; : 9
Successfully executed

Here's the actual script.

program SqrtEx;

function SqrtEx(num: Integer): Extended;
begin
  WriteLn('Original number : ' + IntToStr(num));
  Result := Sqrt(num);
  Result := (((Result + Result) + 5) / 2) - 2.5;
  WriteLn('Number after Result := (((Result + Result) + 5) / 2) - 2.5; : ' + FloatToStr(Result));
end;


begin
SqrtEx(81);
end.

[mixster]

Algebra my good friend helps explain it.
Result + Result + 5 := 2 * Result + 5;
2 * Result + 5 / 2 := Result + 2.5;
Result + 2.5 - 2.5 := Result;

All in all, this function does nothing other than Sqrt

edit:
if nielsie95 = fail then
Writeln('=p');

[nielsie95]

Result := Sqrt(num);
Result := (((Result + Result) + 5) / 2) - 2.5;

You first calculate the Sqrt of the number. Then you do Number * 2 + 5. When you divide by two, you get the number/2 + 5/2, which is number + 2,5. So when you do number - 2,5 you'll get the same number as what you started with, which is the sqrt.

EDIT: aw, mixster beat me

[TViYH]

Oh. Lol. I know algebra, but I thought the way I had the parenthesis aligned changed it. Here's how I thought it would go:

Let's say the original number was 81.

Result := Sqrt(81);
Result := 9;
((Result + Result) + 5) / 2) - 2.5
(18 + 5) / 2) - 2.5
(23 / 2) - 2.5
11.5 - 2.5
9

Am I right?

[mixster]

More or less, that's the way it does it.

[SKy Scripter]

This is how i calculate Sqrt

works up to a 1000...

program new;
var Pn: array [1..1000] of Extended;


procedure LoadSqrt;
var i: Integer;
begin
 for i := 1 to 1000 do
   pn[i] := I * I;
end;


function sqrt2(x: Extended): Extended;
var I, N: Integer;
    e1, e2, e3: extended;
begin
  for i:= 1 to 1000 do
   if (pn[i] > x) then
   begin
       n := i;
       break;
   end;

  e1 := x / n;
  e2 := (e1 + n) div 2;

  while (abs(sqr(e2) - x) > 0.0000001) do
  begin
    e3 := (x / e2)
    e2 := (e2 + e3) / 2;
  end;

  Result := e2;
end;


var k: Integer;
begin
LoadSqrt;
for k:= 1 to 100 do
 Writeln(Floattostr(sqrt2(k)));
 
end.