Question

Part II - Pi Calculation implementation.

• If you watch the Discovery or Sci-Fi channel you will find dozens of alien conspiracy shows that reference Pi as something so advanced that it must be alien.  The number πis a mathematical constant, the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159. So you could graph the value or calculate an approximate value using the series given below:

Pi = 4 * (1/1 – 1/3 + 1/5 – 1/7 + 1/9 … (alternating + -) (1/n))

First, Pi should be a double to allow many decimals. Notice that the numerator is always 1 or -1. If you started the numerator at -1, then multiply each term by -1. So if started the numerator at -1 and multiplied it by -1, the first numerator will be 1, then the next the numerator will be -1, alternating + and -.  

Then notice that the denominator goes from 1,3,5,7,9 etc.  So this is counting by 2s starting at one. For loops are good when you know how many times it will go through the loop. So a for loop might be something like:

for (long denom=1; denom <n; denom=denom+2)
where denom(inator) is the term that changes by 2 starting at 1 (not zero). We use a long to allow very large numbers

• Remember, not every for loop starts at one, and not every for loop ends in i++!
• Also remember that an int divided by int (or long/long) is an int, so you will have to convert the right hand side like double(1/1 – 1/3 + 1/5)
• Note that 4 is multiplied outside the loop (after we have our series determined)

We are using longs, so we can have very long numbers. Likewise, PI should be a double (not a float) to have a very large decimal accuracy

Write a c++ program to calculate the approximate value of pi using this series.  The program takes an input denom that determines the number of values we are going to use in this series.  Then output the approximation of the value of pi. The more values in the series, the more accurate the data.  Note 5 terms isn’t nearly enough to give you an accurate estimation of PI. You will try it with numbers read in from a file. to see the accuracy increase. Use a while loop to read in number of values from a file. Then inside that loop, use a for loop for the calculation.

• Create an input file called lab04in.txt. Place the following numbers in the file. Read in long data types (instead of int)

12

123

1234

12345

123456

1234567

12345678

123456789

• You should work with your lab partner on this, but each of you must write your owncode.
• Implementation Detail 1: Remember that an integer divided by an integer is of type integer (or long/long is a long).  Make sure you use at least one decimal point in your division (like 1.0/9) or double(numerator)/denom
• Implementation Detail 2:The default for the cout of a double is 5 places of accuracy.  If you want to increase that you would use setprecision.  Use setprecision (20)
• http://www.cplusplus.com/reference/iomanip/setprecision/

• Build the program. Fix any errors, then run it. Take a screenshotand place it below

Answer 1

Code

#include<iostream>
#include<fstream>
#include<iomanip>
using namespace std;
long double calculatePi(long n);
int main()
{
   ifstream inFile;
   inFile.open("lab04in.txt");
   long n;
   cout<<fixed<<setprecision(10);
   while(inFile>>n)
   {
       cout<<"For "<<n<<" turms pi= "<<calculatePi(n)<<endl;
   }
}
long double calculatePi(long n)
{
   int count=1;
   long double pi=0;
   for (long denom=1; denom <n; denom++)
   {
       if(denom==1)
       {
           pi =4;   
}
else if(denom%2==0)
{
pi = pi - (4.0/(2.0*denom-1.0));
}
else
       {
           pi = pi+(4.0/(2.0*denom-1.0));
       }
       count++;
}
   return pi;
}

output

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