Preface

"There is a better way to ask!" "There is a better sauce!" I think there are some indications such as. The purpose of this article is to "lead the correct answer by programming". I hope you can see it with warm eyes.

Main subject

What is the Three Square Theorem?

In a right triangle like the image

\begin{equation}a^2+b^2=c^2\end{equation}

Is true.

If you implement this in C # by relying on the Math class ...

//c = a^2 + b^2.
c = Math.Sqrt(Math.Pow(a, 2) + Math.Pow(b, 2));

As mentioned above, it is easy to implement. Pow stands for Power, which is a function that finds the power of a certain value. In this case, we are looking for the squares of the variables ʻa, b. And Sqrt stands for Square root`, which finds a certain number of square roots.

Let's implement these necessary processes on our own.

Power function

//<summary>
//A function that finds the power of a value
//<param name="v1">Value you want to find</param>
//<param name="accuracy">Exponentiation to specify</param>
//</summary>
public static double Power(double v1, Int32 v2)
{
    if (v2 < 1) return 0;

    Int32 counter;
    double result = 1;
    Boolean isNegative = v2 < 0;

    //Assuming the variable is negative
    //nn = v2 < 0 ? (-1) * v2 : v2;Same as above
    if (isNegative)
    {
        counter = (-1) * v2;
    }
    else
    {
        counter = v2;
    }


    for (Int32 j = 0; j < counter; j++)
    {
        result *= v1;
    }

    if (isNegative)
    {
        result = (1 / result);
    }

    return result;
}

SquareRoot function

//<summary>
//Function to find the square root
//<param name="v1">The value for which you want to find the square root</param>
//<param name="accuracy">accuracy. 9~10 is accurate. Initial value 10</param>
//</summary>
public static double SquareRoot(double v1, Int32 accuracy = 10)
{
    if (accuracy < 1) return 0;

    double result = v1;
    for(int x = 0; x < accuracy; x++)
    {
        //result = (result + v1 / result) / 2.Same as 0
        var n1 = v1 / result;
        var n2 = result + n1;
        result = n2 / 2.0;
    }
    return result;
}

Execution result

For confirmation, I compared it with the original one.

Source code:

`Program.cs`


using System;

namespace MathSqrt
{
    class MainClass
    {
        //a^2 + b^2 = c^2
        static double a = 12;
        static double b = 5;
        static double c = 0;
        
        public static void Main(string[] args)
        {
            Console.WriteLine("Hello Math!");

            var na = MyMath.Power(a, 2);
            var nb = MyMath.Power(b, 2);
            c = MyMath.SquareRoot(na+nb);

            Console.WriteLine("Three Square Theorem (Math):{0}", Math.Sqrt(Math.Pow(a, 2) + Math.Pow(b, 2)));
            Console.WriteLine("Three Square Theorem (Square Math):{0}", c);

            Console.ReadKey();
        }
    }
}

Finally

Thank you for watching until the end. If you have any typographical errors / mistakes, please let us know in the comments.

I tried to calculate the Pythagorean theorem (Pythagorean theorem) in C # without relying on an external library