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 alongside $F(n) = n^2$ in C using CLion, you can follow these steps:

1. Break Down the Problem

1. Calculate the Fibonacci numbers from $n = 1$ to $n = 14$.
2. Calculate $F(n) = n^2$ for $n = 1$ to $n = 14$.
3. Use a graphical library or a plotting tool to visualize the results.

2. Relevant Concepts

• Fibonacci Sequence: Defined as: $F(1) = 1, \quad F(2) = 1, \quad F(n) = F(n-1) + F(n-2) \text{ for } n > 2$
• Square Function: Defined as: $F(n) = n^2$

3. Implementation in C

Here's a simple implementation in C to calculate and display the Fibonacci numbers and $n^2$ values:

#include <stdio.h>

// Function to calculate Fibonacci numbers
int fibonacci(int n) {
    if (n <= 1) return n;
    return fibonacci(n - 1) + fibonacci(n - 2);
}

int main() {
    // Arrays to store values
    int n, fib[14], squares[14];

    // Calculate Fibonacci numbers and squares
    for (n = 1; n <= 14; n++) {
        fib[n - 1] = fibonacci(n);
        squares[n - 1] = n * n;
    }

    // Print values
    printf("n\tFibonacci(n)\tn^2\n");
    printf("-----------------------------------\n");
    for (n = 1; n <= 14; n++) {
        printf("%d\t%d\t\t%d\n", n, fib[n - 1], squares[n - 1]);
    }

    return 0;
}

4. Verify and Summarize

• Compile and run your program in CLion.
• The output will display $n$, Fibonacci numbers $F(n)$, and $n^2$ values.

Final Answer

The C code provided computes the Fibonacci numbers and $n^2$ for $n$ from 1 to 14, outputting the results in a tabular format in the console. To plot the results, you might need to redirect the output to a plotting library like GNU Plot or work in an environment that supports graphical output.