Introduction to the Built-In Math Class

Introduction

To help you perform some basic algebraic and geometric operations in your application, the .NET Framework provides a static class named Math. Besides the Math class, you can also take advantage of Visual Basic's very powerful library of functions. This library is one of the most extended set of functions of various area of business mathematics.

Practical LearningPractical Learning: Introducing Math Functions

  1. Start Microsoft Visual Studio and create a new ASP.NET Core Web App named CompoundInterest1 that uses the .NET 6.0 (Long-Term Support). Uncheck the Configure For HTTPS check box
  2. In the Solution Explorer, expand wwwroot
  3. In the Solution Explorer, under wwwroot, right-click css -> Add -> New Item...
  4. In the left list of the Add New Item dialog box, under Visual C#, expand ASP.NET Core. Expand Web, and click Content
  5. In the middle list, click Style Sheet
  6. Change the file Name to CompoundInterest
  7. Press Enter
  8. Change the document as follows: 
    body {
}

.bold        { font-weight:      bold;  }
.text-right  { text-align:       right  }
.delimiter   { margin:           auto;
               width:            650px; }
.top-bar     { border-bottom:    6px solid blue;
               background-color: #5f2c19 !important; }
.common-font { font-family:      Georgia, Garamond, 'Times New Roman', serif; }
.navbar-light .navbar-brand       { color:       white;  }
.navbar-light .navbar-brand:hover { color:       yellow; }
.navbar-light .navbar-brand:focus { color:       khaki;  }
.navbar-light .navbar-brand       { font-family: Georgia, Garamond, 'Times New Roman', serif; }
.nav-link                         { font-family: Georgia, Garamond, 'Times New Roman', serif; }
  9. In the Solution Explorer, expand Pages
  10. In the Solution Explorer, under Pages, expand Shared
  11. In the Solution Explorer, under Pages and under Shared, double-click _Layout.cshtml
  12. Change the document as follows: 
    <!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="utf-8" />
    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
    <title>@ViewData["Title"] - Compound Interest</title>
    <link rel="stylesheet" href="~/lib/bootstrap/dist/css/bootstrap.min.css" />
    <link rel="stylesheet" href="~/css/site.css" asp-append-version="true" />
    <link rel="stylesheet" href="~/css/CompoundInterest.css" asp-append-version="true" />
</head>
<body>
    <header>
        <nav class="navbar navbar-expand-sm navbar-toggleable-sm navbar-light bg-white border-bottom box-shadow mb-3 top-bar">
            <div class="container">
                <a class="navbar-brand" asp-area="" asp-page="/Index">Compound Interest</a>
                <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target=".navbar-collapse" aria-controls="navbarSupportedContent"
                        aria-expanded="false" aria-label="Toggle navigation">
                    <span class="navbar-toggler-icon"></span>
                </button>
                <div class="navbar-collapse collapse d-sm-inline-flex justify-content-between">
                    <ul class="navbar-nav flex-grow-1">
                        <li class="nav-item">
                            <a class="nav-link text-white" asp-area="" asp-page="/Index">Home</a>
                        </li>
                        <li class="nav-item">
                            <a class="nav-link text-white" asp-area="" asp-page="/Privacy">Privacy</a>
                        </li>
                    </ul>
                </div>
            </div>
        </nav>
    </header>
    <div class="container">
        <main role="main" class="pb-3">
            @RenderBody()
        </main>
    </div>

    <footer class="border-top footer text-muted">
        <div class="container">
            <p class="text-center common-font">&copy; 2022 - Compound Interest - <a asp-area="" asp-page="/Privacy">Privacy</a></p>
        </div>
    </footer>

    <script src="~/lib/jquery/dist/jquery.min.js"></script>
    <script src="~/lib/bootstrap/dist/js/bootstrap.bundle.min.js"></script>
    <script src="~/js/site.js" asp-append-version="true"></script>

    @await RenderSectionAsync("Scripts", required: false)
</body>
</html>

The Sign of a Number

When initializing a numeric variable using a constant, you decide whether it is negative, 0 or positive. This is referred to as its sign. To help you determine the sign of a variable or of a number, the Math static class provides a method named Sign(). It is overloaded in various versions for each type. When calling this method, pass the value or the variable you want to consider, as argument. The method returns:

The Integral Side of a Floating-Point Number

We already know that a decimal number consists of an integral side and a precision side; both are separated by the decimal symbol which, in US English, is the period. To let you get the integral side of a decimal value, the Math static class provides a method named Truncate. It is overloaded in two versions whose syntaxes are:

public static double Truncate(double d);
public static double Truncate(double d);

When calling this method, pass it a number or a variable that holds a numeric value. The method returns the int side of the value.

The Minimum of Two Values

If you have two numbers, you can find the minimum of both without writing your own code. To assist you with this, the Math class is equipped with a method named Min. This method is overloaded in various versions with each version adapted to each integral or decimal type.

The Maximum of Two Values

As opposed to the minimum of two numbers, you may be interested in the higher of both. To help you find the maximum of two numbers, the Math class is equipped with a method named Max. It is overloaded in various versions with one for each type of numeric data.

Value Conversions

Implicit Conversions

If you have code with mixed types of variables, you may need to convert a value from one type to another. Implicit conversion is the ability to convert a value of one type into a value of another type. This is possible when the amount of memory that one type is using is lower than the amount necessary for another type. For example, a value of an integer can be directly converted into a double type. Here is an example:

int iNumber = 2445;

double dNumber = iNumber;

In the same way, as saw in our introduction to the double type, you can assign an integral value to a variable of type double. Here is an example:

double number = 927084;

This characteristic is referred to as implicit conversion.

Explicit Conversions

Because of memory requirements, the direct reverse of implicit conversion is not possible. Since the memory reserved for an int variable is smaller than that of a double, you cannot assign a value of type double to a variable of type int. As a result, the following code produces an error:

int hourlySalary = 24.75;

In the same way, you cannot assign a variable of type double to a variable of type int. This means that the following code produces an error:

double nbr = 9270.84;

int number = nbr;

Value Casting

Value casting consists of converting a value of one type into a value of another type. Value casting is also referred to as explicit conversion.

To cast a value or a variable, precede it with the desired data type in parentheses. Here is an example:

double number = 9270.84;

int nbr = (int)number;

When performing explicit conversion, that is, when casting, you should pay close attention to the value that is being cast. If a value cannot fit in the memory of the other, you may get an unpredictable result.

Arithmetic

Absolute Values

The absolute value of a number x is x if the number is (already) positive. If the number is negative, its absolute value is its positive equivalent. To let you get the absolute value of a number, the Math static class is equipped with a method named Abs, which is overloaded in various versions. The syntax for the int and the double types are:

public static int Abs(int value);
public static double Abs(double value);

This method takes the argument whose absolute value must be found.

The Ceiling of a Number

Consider a floating-point number such as 12.155. This number is between integer 12 and integer 13:

Ceiling

In the same way, consider a number such as -24.06. As this number is negative, it is between -24 and -25, with -24 being greater.

In arithmetic, the ceiling of a number is the closest integer that is greater or higher than the number considered. In the first case, the ceiling of 12.155 is 13 because 13 is the closest integer greater than or equal to 12.155. The ceiling of -24.06 is 24.

To support the finding of a ceiling, the Math static class is equipped with a method named Ceiling that is overloaded with two versions. The syntax for a double value is:

public static double Ceiling(double a);

This method takes as argument a number or variable whose ceiling needs to be found. Here is an example:

double value1 = 155.55;
double value2 = -24.06;

double nbr1 = Math.Ceiling(value1));
double nbr2 = Math.Ceiling(value2));

The Floor of a Number

Consider two floating numbers such as 128.44 and -36.72. The number 128.44 is between 128 and 129 with 128 being the lower. The number -36.72 is between -37 and -36 with -37 being the lower. The lowest but closest integer value of a number is referred to as its floor.

To assist you with finding the floor of a number, the Math static class provides the Floor() method. It is overloaded with two versions. The syntax for a double is:

public static double Floor(double d);

The Math.Floor() method takes the considered value as the argument and returns the integer that is less than or equal to the argument. Here is an example:

double value1 = 1540.25;
double value2 = -360.04;

double nbr1 = Math.Floor(value1);
double nbr2 = Math.Floor(value2);

The Power of a Number

The power is the value of one number or expression raised to another number. This follows the formula:

value = xy

To support this operation, the Math static class is equipped with a method named Pow. Its syntax is:

public static double Pow(double x, double y);

This method takes two arguments. The first argument, x, is used as the base number to be evaluated. The second argument, y, also called the exponent, will raise x to this value.

Practical LearningPractical Learning: Getting the Power of a Number

  1. In the Solution Explorer, under Pages, double-click Index.cshtml to open it
  2. Change the document as follows: 
    @page
@model IndexModel
@{
    string strError          = "";
    double periods           = 0.00;
    double principal         = 0.00;
    double interestRate      = 0.00;
    string strFutureValue    = "0.00";
    string strInterestEarned = "0.00";

    if (Request.HasFormContentType)
    {
        try
        {
            principal = double.Parse(Request.Form["txtInitialValue"]);
        }
        catch(FormatException fe)
        {
            strError = "There was an error related to the Principal. The error is as follows: " + 
                        Environment.NewLine + fe.Message;
        }

        try
        {
            interestRate = double.Parse(Request.Form["txtInterestRate"]);
        }
        catch (FormatException fe)
        {
            strError = "The program produced an error related to the interest rate. The error was as follows: " +
                        Environment.NewLine + fe.Message;
        } 

        try
        {
            periods = double.Parse(Request.Form["txtPeriods"]);
        }
        catch (FormatException fe)
        {
            strError = "An error resulted from the value meant for the period. Please report the error as follows: " +
                        Environment.NewLine + fe.Message;
        } 
        
        double frequency   = 12.00;
        double per         = periods / 100;
        double futureValue = principal * Math.Pow((1.00 + (interestRate / frequency)), frequency * per);
        double interestEarned = futureValue - principal;

        strFutureValue = $"{futureValue:F}";
        strInterestEarned       = $"{interestEarned:F}";
    }
}

<h1 class="common-font text-center bold">Compound Interest</h1>       

<hr />

<form name="PayrollEvaluation" method="post" class="common-font delimiter">

<h4>Compound Values:</h4>

<hr />
    <table>
        <tr>
            <td style="width: 150px">@Html.Label("txtInitialValue", "Principal:", new { @class = "bold" })</td>
            <td>@Html.TextBox("txtInitialValue", @principal, new { @class = "form-control" })</td>
            <td>&nbsp;</td>
        </tr>
        <tr>
            <td>@Html.Label("txtInterestRate", "Interest Rate:", new { @class = "bold" })</td>
            <td>@Html.TextBox("txtInterestRate", @interestRate, new { @class = "form-control" })</td>
            <td>%</td>
        </tr>
        <tr>
            <td>@Html.Label("txtPeriods", "Periods:", new { @class = "bold" })</td>
            <td>@Html.TextBox("txtPeriods", @periods, new { @class = "form-control" })</td>
            <td>years</td>
        </tr>
    </table>

    <hr />

    <h4>Compound Frequency:</h4>

    <hr />

    <table>
        <tr>
            <td style="width: 100px"><label for="rdoDaily">Daily</label></td>
            <td><input type="radio" id="rdoDaily" name="rdoFrequency" value="Daily" /></td>
            <td style="width: 50px">&nbsp;</td>
            <td style="width: 100px"><label for="rdoQuaterly">Quaterly</label></td>
            <td><input type="radio" id="rdoQuaterly" name="rdoFrequency" value="Quaterly" /></td>
        </tr>
        <tr>
            <td><label for="rdoWeekly">Weekly</label></td>
            <td><input type="radio" id="rdoWeekly" name="rdoFrequency" value="Weekly" /></td>
            <td>&nbsp;</td>
            <td><label for="rdoSemiannually">Semiannually</label></td>
            <td><input type="radio" id="rdoSemiannually" name="rdoFrequency" value="Semiannually" /></td>
        </tr>
        <tr>
            <td><label for="rdoMonthly">Monthly</label></td>
            <td><input type="radio" id="rdoMonthly" name="rdoFrequency" value="Monthly" /></td>
            <td>&nbsp;</td>
            <td><label for="rdoAnnually">Annually</label></td>
            <td><input type="radio" id="rdoAnnually" name="rdoFrequency" value="Annually" /></td>
        </tr>
    </table>

    <hr />

    <table>
        <tr>
            <td style="width: 150px">&nbsp;</td>
            <td><input type="submit" value="Evaluate Compound Interest" name="btnCalculate" style="width: 250px" /></td>
        </tr>
    </table>

    <hr />
    
    <table>
        <tr>
            <td style="width: 200px" class="bold">Future Value:</td>
            <td style="text-align: right">@strFutureValue</td>
        </tr>
        <tr>
            <td class="bold">Interest Earned:</td>
            <td style="text-align: right">@strInterestEarned</td>
        </tr>
    </table>
</form>
  3. To execute the application, on the main menu, click Debug -> Start Without Debugging:

    Compount Interest

  4. Click the Principal text box and type 5284.65
  5. Click the Interest Rate text box and type 12.35
  6. Click the Periods text box and type 5

    Compount Interest

  7. Click the Evaluate Compound Interest button:

    Compount Interest

  8. Return to your programming environment, press Enter
  9. Change the Index.cshtml document as follows: 
    @page
@model IndexModel
@{
    string strError          = "";
    double periods           = 0.00;
    double principal         = 0.00;
    double interestRate      = 0.00;
    string strFutureValue    = "0.00";
    string strInterestEarned = "0.00";
    string strFrequency      = "";

    if (Request.HasFormContentType)
    {
        try
        {
            principal = double.Parse(Request.Form["txtInitialValue"]);
        }
        catch(FormatException fe)
        {
            strError = "There was an error related to the Principal. The error is as follows: " + 
                        Environment.NewLine + fe.Message;
        }

        try
        {
            interestRate = double.Parse(Request.Form["txtInterestRate"]);
        }
        catch (FormatException fe)
        {
            strError = "The program produced an error related to the interest rate. The error was as follows: " +
                        Environment.NewLine + fe.Message;
        } 

        try
        {
            periods = double.Parse(Request.Form["txtPeriods"]);
        }
        catch (FormatException fe)
        {
            strError = "An error resulted from the value meant for the period. Please report the error as follows: " +
                        Environment.NewLine + fe.Message;
        } 


        double frequency   = 12.00;
        
        strFrequency = Request.Form["rdoFrequency"];

        switch (strFrequency)
        {
            case "Daily":
                frequency = 365.00;
                break;
            case "Weekly":
                frequency = 52.00;
                break;
            case "Monthly":
                frequency = 12.00;
                break;    
            case "Quaterly":
                frequency = 4.00;
                break;
            case "Semiannually":
                frequency = 2.00;
                break;
            case "Annually":
                frequency = 1.00;
                break;
        }

        double per            = periods / 100;
        double futureValue    = principal * Math.Pow((1.00 + (interestRate / frequency)), frequency * per);
        double interestEarned = futureValue - principal;

        strFutureValue        = $"{futureValue:F}";
        strInterestEarned     = $"{interestEarned:F}";
    }
}

<h1 class="common-font text-center bold">Compound Interest</h1>       

<hr />

<form name="PayrollEvaluation" method="post" class="common-font delimiter">

<h4>Compound Values:</h4>

<hr />
    <table>
        <tr>
            <td style="width: 150px">@Html.Label("txtInitialValue", "Principal:", new { @class = "bold" })</td>
            <td>@Html.TextBox("txtInitialValue", @principal, new { @class = "form-control" })</td>
            <td>&nbsp;</td>
        </tr>
        <tr>
            <td>@Html.Label("txtInterestRate", "Interest Rate:", new { @class = "bold" })</td>
            <td>@Html.TextBox("txtInterestRate", @interestRate, new { @class = "form-control" })</td>
            <td>%</td>
        </tr>
        <tr>
            <td>@Html.Label("txtPeriods", "Periods:", new { @class = "bold" })</td>
            <td>@Html.TextBox("txtPeriods", @periods, new { @class = "form-control" })</td>
            <td>years</td>
        </tr>
    </table>

    <hr />

    <h4>Compound Frequency:</h4>

    <hr />

    <table>
        <tr>
            <td style="width: 100px"><label for="rdoDaily">Daily</label></td>
            <td><input type="radio" id="rdoDaily" name="rdoFrequency" value="Daily" /></td>
            <td style="width: 50px">&nbsp;</td>
            <td style="width: 100px"><label for="rdoQuaterly">Quaterly</label></td>
            <td><input type="radio" id="rdoQuaterly" name="rdoFrequency" value="Quaterly" /></td>
        </tr>
        <tr>
            <td><label for="rdoWeekly">Weekly</label></td>
            <td><input type="radio" id="rdoWeekly" name="rdoFrequency" value="Weekly" /></td>
            <td>&nbsp;</td>
            <td><label for="rdoSemiannually">Semiannually</label></td>
            <td><input type="radio" id="rdoSemiannually" name="rdoFrequency" value="Semiannually" /></td>
        </tr>
        <tr>
            <td><label for="rdoMonthly">Monthly</label></td>
            <td><input type="radio" id="rdoMonthly" name="rdoFrequency" value="Monthly" /></td>
            <td>&nbsp;</td>
            <td><label for="rdoAnnually">Annually</label></td>
            <td><input type="radio" id="rdoAnnually" name="rdoFrequency" value="Annually" /></td>
        </tr>
    </table>

    <hr />

    <table>
        <tr>
            <td style="width: 150px">&nbsp;</td>
            <td><input type="submit" value="Evaluate Compound Interest" name="btnCalculate" style="width: 250px" /></td>
        </tr>
    </table>

    <hr />
    
    <table>
        <tr>
            <td style="width: 200px" class="bold">Compound Frequency:</td>
            <td style="text-align: right">@strFrequency</td>
        </tr>
        <tr>
            <td class="bold">Future Value:</td>
            <td style="text-align: right">@strFutureValue</td>
        </tr>
        <tr>
            <td class="bold">Interest Earned:</td>
            <td style="text-align: right">@strInterestEarned</td>
        </tr>
    </table>
</form>
  10. To execute the application, on the main menu, click Debug -> Start Without Debugging
  11. If the browser presents a Resend button, click it, or refresh the browser
  12. Click each of the radio buttons and click the Evaluate Compound Interest button:

    Compount Interest

    Compount Interest

    Compount Interest

  13. Close the browser and return to your programming environment, press Enter
  14. Save the following images to your computer:

    Polygons - Square

    Polygons - Equilateral Triangle

  15. Start a new ASP.NET Core Web App named Geometry3 that uses the .NET 6.0 (Long-Term Support). Uncheck the Configure For HTTPS check box
  16. In the Solution Explorer, right-click Geometry3 -> Add -> New Folder
  17. Type Models
  18. In the Solution Explorer, right-click wwwroot -> Add -> New Folder
  19. Type images and press Enter
  20. In the Solution Explorer, under wwwroot, right-click images -> Add -> Existing Item...
  21. Select the above images, then select the trapezoid1.png and the tp.png images you had saved in previous lessons. Add them to the project
  22. In the Solution Explorer, under wwwroot, right-click css -> Add -> New Item...
  23. In the left list of the Add New Item dialog box, under Visual C#, expand ASP.NET Core. Expand Web, and click Content
  24. In the middle list, click Style Sheet
  25. Change the file Name to Geometry
  26. Press Enter
  27. Change the document as follows: 
    body {
}

.bold        { font-weight:      bold;  }
.text-right  { text-align:       right  }
.delimiter   { margin:           auto;
               width:            650px; }
.top-bar     { border-bottom:    6px solid blue;
               background-color: #0046be !important; }
.common-font { font-family:      Georgia, Garamond, 'Times New Roman', serif; }
.navbar-light .navbar-brand       { color:       white;  }
.navbar-light .navbar-brand:hover { color:       yellow; }
.navbar-light .navbar-brand:focus { color:       khaki;  }
.navbar-light .navbar-brand       { font-family: Georgia, Garamond, 'Times New Roman', serif; }
.nav-link                         { font-family: Georgia, Garamond, 'Times New Roman', serif; }
  28. In the Solution Explorer, expand Pages
  29. In the Solution Explorer, under Pages, expand Shared
  30. In the Solution Explorer, under Pages and under Shared, double-click _Layout.cshtml
  31. Change the document as follows: 
    <!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="utf-8" />
    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
    <title>@ViewData["Title"] - Geometry</title>
    <link rel="stylesheet" href="~/lib/bootstrap/dist/css/bootstrap.min.css" />
    <link rel="stylesheet" href="~/css/site.css" asp-append-version="true" />
    <link rel="stylesheet" href="~/css/Geometry.css" asp-append-version="true" />
</head>
<body>
    <header>
        <nav class="navbar navbar-expand-sm navbar-toggleable-sm navbar-light bg-white border-bottom box-shadow mb-3 top-bar">
            <div class="container">
                <a class="navbar-brand" asp-area="" asp-page="/Index">Geometry</a>
                <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target=".navbar-collapse" aria-controls="navbarSupportedContent"
                        aria-expanded="false" aria-label="Toggle navigation">
                    <span class="navbar-toggler-icon"></span>
                </button>
                <div class="navbar-collapse collapse d-sm-inline-flex justify-content-between">
                    <ul class="navbar-nav flex-grow-1">
                        <li class="nav-item">
                            <a class="nav-link text-white" asp-area="" asp-page="/Square">Square</a>
                        </li>
                        <li class="nav-item">
                            <a class="nav-link text-white" asp-area="" asp-page="/EquilateralTriangle">Equilateral Triangle</a>
                        </li>
                        <li class="nav-item">
                            <a class="nav-link text-white" asp-area="" asp-page="/Trapezoid">Trapezoid</a>
                        </li>
                        <li class="nav-item">
                            <a class="nav-link text-white" asp-area="" asp-page="/TrapezoidalPrism">Trapezoid Prism</a>
                        </li>
                    </ul>
                </div>
            </div>
        </nav>
    </header>
    <div class="container">
        <main role="main" class="pb-3">
            @RenderBody()
        </main>
    </div>

    <footer class="border-top footer text-muted">
        <div class="container">
            <p class="text-center common-font">&copy; 2022 - Geometry - <a asp-area="" asp-page="/Privacy">Privacy</a></p>
        </div>
    </footer>

    <script src="~/lib/jquery/dist/jquery.min.js"></script>
    <script src="~/lib/bootstrap/dist/js/bootstrap.bundle.min.js"></script>
    <script src="~/js/site.js" asp-append-version="true"></script>

    @await RenderSectionAsync("Scripts", required: false)
</body>
</html>

The Exponential

To let you calculate the exponential value of a number, the Math static class provides the Exp() method. Its syntax is:

public static double Exp(double d);

If the value of the argument x is less than -708.395996093 (approximately), the result is reset to 0 and qualifies as underflow. If the value of the argument x is greater than 709.78222656 (approximately), the result qualifies as overflow.

Here is an example of calling this method:

<pre<The exponential of 709.78222656 is @(Math.Exp(709.78222656)</pre>

This would produce:

The exponential of 709.78222656 is 1.79681906923757E+308

The Natural Logarithm

To calculate the natural logarithm of a number, you can call the Math.Log() method. It is provides in two versions. The syntax of one is:

public static double Log(double d);

Here is an example:

@{
    double log = 12.48;
}

<pre<Log of @log is @(Math.Log(log)</pre>

This would produce:

Log of 12.48 is 2.52412736294128

The Base 10 Logarithm

The Math.Log10() method calculates the base 10 logarithm of a number. The syntax of this method is:

public static double Log10(double d);

The number to be evaluated is passed as the argument. The method returns the logarithm on base 10 using the formula:

y = log10x

which is equivalent to

x = 10y

Here is an example:

@{
    double log10 = 12.48;
}

<pre<Log 10 of @log10 is @(Math.Log10(log10)</pre>

This would produce:

Log 10 of 12.48 is 1.09621458534641

The Logarithm of Any Base

The Math.Log() method provides another version whose syntax is:

public static double Log(double a, double newBase);

The variable whose logarithmic value will be calculated is passed as the first argument to the method. The second argument allows you to specify a base of your choice. The method uses the formula:

Y = logNewBasex

This is the same as

x = NewBasey

Here is an example of calling this method:

@{
        double logN = 12.48D;
}

<pre<Log N of @logN is @(Math.Log(logN, 4)</pre>

This would produce:

Log N of 12.48 is 1.82077301454376

The Square Root

You can calculate the square root of a decimal positive number. To support this, the Math static class is equipped with a method named Sqrt whose syntax is:

public static double Sqrt(double d);

This method takes one argument as a positive floating-point number. After the calculation, the method returns the square root of x:

@{
    double sqrt = 8025.73;

    double number = Math.Sqrt(sqrt));
}

ApplicationPractical Learning: Finding the Square Root of a Number

  1. In the Solution Explorer, right-click Models -> Add -> Class...
  2. In the middle list of the Add New Item dialog box, make sure Class is selected.
    Change the suggested name to Square
  3. Click Add
  4. Change the Square class as follows: 
    namespace Geometry3.Models
{
    public class Square
    {
        public double Side { get; set; }

        public Square(double side)
        {
            Side = side;
        }

        public double Perimeter
        {
            get
            {
                return Side * 4.00;
            }
        }

        public virtual double Area
        {
            get
            {
                return Side * Side;
            }
        }

        public virtual double CalculateInradius()
        {
            return Side / 2.00;
        }

        public virtual double CalculateCircumradius()
        {
            return Math.Sqrt(2.00) * Side / 2.00;
        }
    }
}
  5. In the Solution Explorer, right-click Pages -> Add -> Razor Page...
  6. In the middle list of the Add New Scaffolded Item dialog box, make sure Razor Page - Empty is selected.
    Press Enter
  7. Change the file name to Square
  8. Click Add
  9. Change the document as follows: 
    @page
@model Geometry3.Pages.SquareModel
@using Geometry3.Models
@{
    double side = 0.00;
    string? strMessage = null;
    Square sqr = new Square(0.00);

    if (Request.HasFormContentType)
    {
        try
        {
            side = double.Parse(Request.Form["txtSide"])!;
        }
        catch(FormatException fexc)
        {
            strMessage = "You must provide a valid value for the side of the square." + 
                         Environment.NewLine + "The error produced is: " + 
                         fexc.Message;
        }

        sqr = new(side);
    }
}

<div class="delimiter common-font">
    <h2 class="text-center bold">Geometry - Polygon - Square</h2>
    <hr />
   <form name="frmGeometry" method="post">
      <table>
          <tr>
              <td style="width: 400px" rowspan="8">
                  <img src="~/images/triangle1.png" width="391" height="315" alt="Geometry - Square">
              </td>
              <td style="width: 150px" class="bold">Side:</td>
              <td>@Html.TextBox("txtSide", @sqr.Side, new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td>&nbsp;</td>
              <td style="text-align: center"><input type="submit" name="btnSubmit" value="Calculate" /></td>
          </tr>
          <tr>
              <td class="bold">Perimeter:</td>
              <td class="text-right">@sqr.Perimeter</td>
          </tr>
          <tr>
              <td class="bold">Area:</td>
              <td class="text-right">@sqr.Area</td>
          </tr>
          <tr>
              <td class="bold">Inradius:</td>
              <td class="text-right">@sqr.CalculateInradius()</td>
          </tr>
          <tr>
              <td class="bold">Circumradius:</td>
              <td class="text-right">@sqr.CalculateCircumradius()</td>
          </tr>
      </table>
  </form>

  <hr />
  <p class="text-center">@strMessage</p>
</div>
  10. In the Solution Explorer, right-click Models -> Add -> Class...
  11. In the middle list of the Add New Item dialog box, make sure Class is selected.
    Change the file Name to EquilateralTriangle
  12. Press Enter
  13. Change the document as follows: 
    namespace Geometry3.Models
{
    public class EquilateralTriangle
    {
        private double s;
        public readonly double NumberOfSides;

        public EquilateralTriangle(double side)
        {
            s = side;
            NumberOfSides = 3;
        }

        public double Side
        {
            get { return s;  }
            set { s = value; }
        }

        public double Perimeter    => s * NumberOfSides;
        public double Height       => s * Math.Sqrt(3) / 2;
        public double Area         => s * s * Math.Sqrt(3) / 4;
        public double Inradius     => s * Math.Sqrt(3) / 6;
        public double Circumradius => s / Math.Sqrt(3);
    }
}
  14. In the Solution Explorer, right-click Pages -> Add -> Razor Page...
  15. In the middle list of the Add New Scaffolded Item dialog box, make sure Razor -Page - Empty is selected.
    Click Add
  16. Change the file Name to EquilateralTriangle
  17. Click Add
  18. Change the document as follows: 
    @page
@model Geometry3.Pages.EquilateralTriangleModel
@using Geometry3.Models
@{
    double side = 0.00;
    string? strMessage = null;
    EquilateralTriangle et = new(0.00);

    if (Request.HasFormContentType)
    {
        try
        {
            side = double.Parse(Request.Form["txtSide"])!;
        }
        catch(FormatException fexc)
        {
            strMessage = "You must provide a valid common value for the sides of the triangle." + 
                         Environment.NewLine + "The error produced is: " + 
                         fexc.Message;
        }

        et = new(side);
    }
}

<div class="delimiter common-font">
    <h2 class="text-center bold">Geometry - Equilateral Triangle</h2>
    <hr />
   <form name="frmGeometry" method="post">
      <table>
          <tr>
              <td style="width: 400px" rowspan="8">
                  <img src="~/images/triangle1.png" width="391" height="315" alt="Geometry - Square">
              </td>
              <td style="width: 150px" class="bold">Side:</td>
              <td>@Html.TextBox("txtSide", @et.Side, new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td>&nbsp;</td>
              <td style="text-align: center"><input type="submit" name="btnSubmit" value="Calculate" /></td>
          </tr>
          <tr>
              <td class="bold">Number of Sides:</td>
              <td class="text-right">@et.NumberOfSides</td>
          </tr>
          <tr>
              <td class="bold">Height:</td>
              <td class="text-right">@et.Height</td>
          </tr>
          <tr>
              <td class="bold">Perimeter:</td>
              <td class="text-right">@et.Perimeter</td>
          </tr>
          <tr>
              <td class="bold">Area:</td>
              <td class="text-right">@et.Area</td>
          </tr>
          <tr>
              <td class="bold">Inradius:</td>
              <td class="text-right">@et.Inradius</td>
          </tr>
          <tr>
              <td class="bold">Circumradius:</td>
              <td class="text-right">@et.Circumradius</td>
          </tr>
      </table>
  </form>

  <hr />
  <p class="text-center">@strMessage</p>
</div>
  19. In the Solution Explorer, right-click Models -> Add -> Clas...
  20. In the middlelist of the Add New Item dialog box, make sure Class is selected.
    Change the Name of the file to Trapezoid
  21. Click Add
  22. Change the class as follows: 
    namespace Geometry3.Models
{
    public class Trapezoid
    {
        public double Edge      { get; set; }
        public double ShortWidth { get; set; }
        public double LargeWidth { get; set; }

        public Trapezoid(double sSide, double lSide, double edge)
        {
            Edge       = edge;
            LargeWidth = lSide;
            ShortWidth = sSide;
        }

        public double Perimeter => LargeWidth + Edge + ShortWidth + Edge;

        // http://mathworld.wolfram.com/IsoscelesTrapezoid.html
        public double Height
        {
            get
            {
                return Math.Sqrt((Edge * Edge) - (Math.Pow(LargeWidth - ShortWidth, 2.00) / 4.00));
            }
        }

        virtual public double CalculateArea()
        {
            return (LargeWidth + ShortWidth) * Height / 2.00;
        }
    }
}
  23. In the Solution Explorer, right-click Pages -> Add -> Razor Page...
  24. In the middle list of the Add New Scaffolded Item dialog box, make sure Razor Page - Empty is selected.
    Click Add
  25. Change the file Name to Trapezoid
  26. Click Add
  27. Cchange the document as follows: 
    @page
@model Geometry3.Pages.TrapezoidModel
@using Geometry3.Models
@{
    string? strMessage = null;
    Trapezoid trap = new(0.00, 0.00, 0.00);

    if (Request.HasFormContentType)
    {
        try
        {
            trap.ShortWidth = double.Parse(Request.Form["txtShortWidth"]);
        }
        catch(FormatException fexc)
        {
            strMessage = fexc.Message;
        }

        try
        {
            trap.LargeWidth = double.Parse(Request.Form["txtLargeWidth"]);
        }
        catch(FormatException fexc)
        {
            strMessage = fexc.Message;
        }

        try
        {
            trap.Edge = double.Parse(Request.Form["txtEdge"]);
        }
        catch(FormatException fexc)
        {
            strMessage = fexc.Message;
        }
    }
}

<div class="delimiter common-font">
    <h2 class="text-center bold">Geometry - Trapezoid</h2>
    <hr />
   <form name="frmGeometry" method="post">
      <table>
          <tr>
              <td style="width: 300px" rowspan="9">
                  <img src="~/images/trapezoid1.png" width="296" height="247" alt="Geometry - Trapezoid">
              </td>
              <td style="width: 125px" class="bold">Short Width:</td>
              <td>@Html.TextBox("txtShortWidth", @trap.ShortWidth, new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td class="bold">Large Width:</td>
              <td>@Html.TextBox("txtLargeWidth", @trap.LargeWidth, new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td class="bold">Edge:</td>
              <td>@Html.TextBox("txtEdge", @trap.Edge, new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td>&nbsp;</td>
              <td style="text-align: center"><input type="submit" name="btnSubmit" value="Calculate" /></td>
          </tr>
          <tr>
              <td class="bold">Height:</td>
              <td>@Html.TextBox("txtHeight", @trap.Height, new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td class="bold">Area:</td>
              <td>@Html.TextBox("txtArea", @trap.CalculateArea(), new { @class = "form-control text-right" })</td>
          </tr>
      </table>
  </form>

  <hr />
  <p class="text-center">@strMessage</p>
</div>
  28. In the Solution Explorer, right-click Models -> Add -> Class...
  29. Make sure Class is selected in the Add New Item dialog box.
    Change the file Name to TrapezoidalPrism
  30. Click Add
  31. Change the class as follows: 
    namespace Geometry3.Models
{
    public class TrapezoidalPrism : Trapezoid
    {
        public double Length { get; set; }

        public TrapezoidalPrism(double sSide, double lSide, double side, double len)
                : base(sSide, lSide, side)
        {
            Length = len;
        }

        public double BaseArea => base.CalculateArea();

        override public double CalculateArea()
        {
            double shortArea = ShortWidth * Length;
            double longArea  = LargeWidth * Length;
            double sideArea  = Edge       * Length;
            return (BaseArea * 2.00) + shortArea + longArea + (sideArea * 2.00);
        }

        public double Volume => BaseArea * Length;
    }
}
  32. To start a new razor page, in the Solution Explorer, right-click Pages -> Add -> Razor Page...
  33. In the Add New Scaffolded Item dialog box, makew sure Razor Page - Empty is selected and click Add
  34. Change the file Name to TrapezoidalPrism
  35. Press Enter
  36. Change the document as follows: 
    @page
@model Geometry3.Pages.TrapezoidalPrismModel
@using Geometry3.Models
@{
    string? strMessage = null;
    TrapezoidalPrism trap = new TrapezoidalPrism(0.00, 0.00, 0.00, 0.00);

    if (Request.HasFormContentType)
    {
        try
        {
            trap.ShortWidth = double.Parse(Request.Form["txtShortWidth"]);
        }
        catch(FormatException fexc)
        {
            strMessage = fexc.Message;
        }
        try
        {
            trap.LargeWidth = double.Parse(Request.Form["txtLargeWidth"]);
        }
        catch(FormatException fexc)
        {
            strMessage = fexc.Message;
        }
        try
        {
            trap.Edge = double.Parse(Request.Form["txtEdge"]);
        }
        catch(FormatException fexc)
        {
            strMessage = fexc.Message;
        }
        try
        {
            trap.Length = double.Parse(Request.Form["txtLength"]);
        }
        catch(FormatException fexc)
        {
            strMessage = fexc.Message;
        }
    }
}

<div class="delimiter common-font">
    <h2 class="text-center bold">Geometry - Trapezoidal Prism</h2>
    <hr />
   <form name="frmGeometry" method="post">
      <table>
          <tr>
              <td style="width: 300px" rowspan="9">
                  <img src="~/images/tp.png" width="289" height="230" alt="Geometry - Trapezoidal Prism">
              </td>
              <td style="width: 125px" class="bold">Short Width:</td>
              <td>@Html.TextBox("txtShortWidth", @trap.ShortWidth, new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td class="bold">Large Width:</td>
              <td>@Html.TextBox("txtLargeWidth", @trap.LargeWidth, new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td class="bold">Edge:</td>
              <td>@Html.TextBox("txtEdge", @trap.Edge, new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td class="bold">Length:</td>
              <td>@Html.TextBox("txtLength", @trap.Length, new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td>&nbsp;</td>
              <td style="text-align: center"><input type="submit" name="btnSubmit" value="Calculate" /></td>
          </tr>
          <tr>
              <td class="bold">Base Area:</td>
              <td>@Html.TextBox("txt>BaseArea", @trap.BaseArea, new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td class="bold">Total Area:</td>
              <td>@Html.TextBox("txtTotalArea", @trap.CalculateArea(), new { @class = "form-control text-right" })</td>
          </tr>
          <tr>
              <td class="bold">Volume:</td>
              <td>@Html.TextBox("txtVolume", @trap.Volume, new { @class = "form-control text-right" })</td>
          </tr>
      </table>
  </form>

  <hr />
  <p class="text-center">@strMessage</p>
</div>
  37. To execute the application to test it, on the main menu, click Debug -> Start Without Debugging
  38. Click the Square link:

    Mathematical Functions - Square

  39. Click the Side text box and type 837.59

    Mathematical Functions - Square

  40. Click the Calculate button:

    Mathematical Functions - Square

  41. Click the Equilateral Triangle link:

    Mathematical Functions

  42. Click the Side text box and type 309.66

    Mathematical Functions

  43. Click the Calculate button:

    Mathematical Functions

  44. Click the Trapezoid link

    Mathematical Functions

  45. Click the Short Width text box and type 137.96
  46. Click the Large Width text box and type 209.73
  47. Click the Edge text box and type 87.59

    Mathematical Functions

  48. Click the Calculate button

    Mathematical Functions

  49. Click the Trapezoidal Prism link

    Mathematical Functions

  50. Click the Short Width text box and type 229.47
  51. Click the Large Width text box and type 167.66
  52. Set the Edge value to 98.59
  53. For the Length, type 214.85

    Mathematical Functions

  54. Click theb Calculate button

    Mathematical Functions

  55. Close the browser and return to your programming environment
  56. Close your programming environment
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