Plot the Fibonacci numbers from n = 1 to 14, together with F(n) = n^2 use clion by c codes

To plot the Fibonacci numbers from $n = 1$ to $14$ along with $F(n) = n^2$ using C in CLion, you can follow the steps below.

Step 1: Install Required Libraries

First, ensure you have the gnuplot library or any other graphing library to visualize the data. You can use gnuplot to plot from the terminal.

Step 2: Write the C Program

Create a new C file and include logic to generate Fibonacci numbers and $n^2$ values.

#include <stdio.h>

void generateFibonacci(int n, int fib[]) {
    fib[0] = 0; // F(0)
    fib[1] = 1; // F(1)
    for (int i = 2; i <= n; i++) {
        fib[i] = fib[i - 1] + fib[i - 2];
    }
}

int main() {
    int n = 14; // We want Fibonacci numbers up to F(14)
    int fib[15]; // Array to hold Fibonacci numbers
    
    // Generate Fibonacci numbers
    generateFibonacci(n, fib);
    
    // Open a file to write data
    FILE *fptr = fopen("data.txt", "w");
    if (fptr == NULL) {
        printf("Error opening file.\n");
        return 1;
    }

    // Write Fibonacci and n^2 values to file
    for (int i = 1; i <= n; i++) {
        fprintf(fptr, "%d %d %d\n", i, fib[i], i * i); // n, F(n), n^2
    }
    
    fclose(fptr);
    printf("Data written to data.txt\n");

    return 0;
}

Step 3: Compile and Run the Program

1. Open CLion and create a new project.
2. Copy the code into a .c file.
3. Build and run the program. This will generate the data.txt file with the values.

Step 4: Plot Using Gnuplot

1. After running your C program, you will have a file named data.txt that contains the calculated Fibonacci numbers and corresponding $n^2$ values.
2. Open gnuplot in terminal and execute the following commands:

set title "Fibonacci Sequence and n^2"
set xlabel "n"
set ylabel "Values"
set key outside
plot "data.txt" using 1:2 title "F(n) = Fibonacci", \
     "" using 1:3 title "F(n) = n^2" with lines

Summary

In this code, we generated the Fibonacci numbers and their squares, saved them to a text file, and then plotted them using gnuplot. Make sure you have gnuplot installed on your machine to visualize the data after generating it with the program.

Final Answer

The C program outputs the Fibonacci numbers and $F(n) = n^2$ values to a data.txt file, which can be plotted using gnuplot.