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C Brain Teasers: Exercise Your Mind

Discussion: Calculating Nested Values

Discover how to calculate the value of pi using a recursive function that implements a generalized continued fraction in C. Learn the logic behind this mathematical concept translated into code, enhancing your understanding of recursion and numeric computations in programming.

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Run the code

Now, it's time to execute the code and observe the output.

C
#include <stdio.h>
float p(float a, float b)
{
  return((b<100.0)?a+(b*b/p(a+2.0, b+1.0)):b*b);
}
int main()
{
  printf("%.7f\n", 4.0/p(1.0, 1.0));
  return(0);
}

Understanding the output

3.1415925
Code output

How the code generates this output, especially without using any trigonometric functions, is the story to tell.

The story

Calculating π (pi), the ratio of a circle’s diameter to its circumference, is an age-old computer programming task. It was also the subject of a Star Trek episode where Mr. Spock directed the computer to “calculate to the last digit the value of pi.” Of course, the computer got busy with the project to the point of pushing out an evil entity. Computers can do amazing things!

The question isn’t whether a computer can calculate the value of π but how? To assist the programmer, various mathematical theorems are available. Each of these is clever and cryptic, though the point is ...