Math.LOG2E 1.442695040888963387 Log base-2 of E Math.Log10E 0.4342944819032518167 Log base-10 of E Math.PI 3.14592653589793116 Pi, ratio of the circumference of a circle to its diam
Trang 19.5 The Math Object
The Math object allows you to work with more advanced arithmetic calculations, such
as square root, trigonometric functions, logarithms, and random numbers, than are
pro-vided by the basic numeric operators If you are doing simple calculations, you really
won’t need it
Unlike other objects, you don’t have to create an instance of the Math object with the
new keyword It is a built-in object and has a number of properties (see Table 9.5) and
methods (see Table 9.6) The Math object always starts with an uppercase M
E X P L A N A T I O N
1 The function called weekDay() is defined.
2 The variable now is assigned a number representing the day of the week, where 0
is Sunday
3 A new Array object called names is created It will contain seven elements Each
element will be assigned the name of the weekday (e.g., “Sunday”).
4 The value in now, a number between 0 and 6, will be used as an index in the names
array If now is 6, then the value of names[6], “Saturday”, will be returned.
5 A prototype method called DayOfWeek is assigned the name of the function
week-Day Now the Date object has a new method that will be inherited by all objects
created from the Date() constructor The capabilities of the Date object have been
extended to provide a method that will return the name of the weekday (See
Chapter 8 for more on prototypes.)
6 A new Date object is created with the Date() constructor function.
7 The new prototype method is called, and returns the string value of today’s date,
“Saturday” (see Figure 9.23)
Figure 9.23 The day is converted to a string using a prototype.
Table 9.5 Math Object Properties
Math.E 2.718281828459045091 Euler’s constant, the base of
natural logarithms
Math.LN2 0.6931471805599452862 Natural log of 2
Math.LN10 2.302585092994045901 Natural log of 10
Continues
Trang 2Math.LOG2E 1.442695040888963387 Log base-2 of E
Math.Log10E 0.4342944819032518167 Log base-10 of E
Math.PI 3.14592653589793116 Pi, ratio of the circumference of a
circle to its diameter
Math.SQRT1_2 0.7071067811865475727 1 divided by the square root of 2
Math.SQRT2 1.414213562373985145 Square root of 2
Table 9.6 Math Object Methods
Math.abs(Number) Returns the absolute (unsigned) value of Number
Math.acos(Number) Arc cosine of Number, returns result in radians
Math.asin(Number) Arc sine of Number, returns results in radians
Math.atan(Number) Arctangent of Number, returns results in radians
Math.atan2(y,x) Arctangent of y/x; returns arctangent of the quotient of its
arguments
Math.ceil(Number) Rounds Number up to the next closest integer
Math.cos(Number) Returns the cosine of Number in radians
Math.exp(x)* Euler’s constant to some power
Math.floor(Number) Rounds Number down to the next closest integer
Math.log(Number) Returns the natural logarithm of Number (base E)
Math.max(Number1, Number2) Returns larger value of Number1 and Number2
Math.min(Number1, Number2) Returns smaller value of Number1 and Number2
Math.pow(x, y) Returns the value of x to the power of y(x y ), where x is the
base and y is the exponent Math.random() Generates pseudorandom number between 0.0 and 1.0
Math.round(Number) Rounds Number to the closest integer
Math.sin(Number) Arc sine of Number in radians
Math.sqrt(Number) Square root of Number
Table 9.5 Math Object Properties (continued)
Trang 3Square Root, Power of, and Pi. The Math object comes with a number of common
mathematical constants (all uppercase), such as PI and natural log values, as well as
meth-ods to find the square root of a number, the power of a number, and so on Example 9.20
demonstrates how to use some of these properties; the output is shown in Figure 9.24
Math.tan(Number) Tangent of Number in radians
Math.toString(Number) Converts Number to string
* Returns the value of E x where E is Euler’s constant and x is the argument passed to it Euler’s constant is
approximately 2.7183.
E X A M P L E 9 2 0
<html>
<head><title>The Math Object</title></head>
<body>
<h2>Math object Methods sqrt(),pow()<br />
Math object Property PI
</h2>
<h3>
<script type="text/javascript">
document.write("The square root of " +num+ " is ");
document.write(Math.sqrt(num),".<br />");
2 document.write("PI is ");
document.write(".<br />"+num+" raised to the 3rd power is " );
4 document.write(Math.pow(num,3) + ".");
</script>
</h3>
</body>
</html>
E X P L A N A T I O N
1 The number 16 will be manipulated by Math methods and constants.
2 The Math object’s sqrt() method returns the square root of number 16, which is 4.
3 The Math object’s PI constant produces the value of PI.
4 The Math object’s pow() methods raises and returns number 16 to the 3rd power,
which is 4096 (see Figure 9.24)
Table 9.6 Math Object Methods (continued)
Trang 4There are three Math methods available for rounding numbers up or down They are the
ceil(), floor(), and round() methods (see Table 9.7 for examples) The differences among the
methods might be confusing because all three methods truncate the numbers after the
dec-imal point and return a whole number If you recall, JavaScript also provides the parseInt()
function, but this function truncates the number after the decimal point, without rounding
either up or down
The ceil() Method The ceil() method rounds a number up to the next largest whole
number and then removes any numbers after the decimal point; thus, 5.02 becomes 6
because 6 is the next largest number, and –5.02 becomes –5 because –5 is larger than –6
The floor() Method The floor() method rounds a number down to the next lowest
whole number and then removes any numbers after the decimal point; thus, 5.02 now
becomes 5, and –5.02 becomes –6
The round() Method The round() method rounds up only if the decimal part of the
number is 5 or greater Otherwise, it rounds down to the nearest integer; thus, 5.5 is
rounded up to 6, and 5.4 is rounded down to 5
Figure 9.24 The Math object, some properties and methods.
Table 9.7 Rounding up and down
Number ceil() floor() round()
Trang 5Random numbers are frequently used in JavaScript programs to produce random images
(such as banners streaming across a screen), random messages, or random numbers
E X A M P L E 9 2 1
<html>
<head><title>The Math Object</title></head>
<body>
<h2>Rounding Numbers</h2>
<p>
<h3>
<script type="text/javascript">
document.write("<I>The number being manipulated is: ", num,
"</I><br /><br />");
2 document.write("The <I>Math.floor</I> method rounds down: "
+ Math.floor(num) + "<br />");
3 document.write("The <I>Math.ceil</I> method rounds up: " +
Math.ceil(num) +"<br />");
4 document.write("The <I>Math.round</I> method rounds to\
the nearest integer: " + Math.round(num) + "<br />");
</script>
</h3>
</body>
</html>
E X P L A N A T I O N
1 The number 16.3 will be manipulated by the Math object’s methods.
2 The Math object’s floor() method rounds the number down to the next lowest
whole number 16.3 rounds down to 16
3 The Math object’s ceil() method rounds a number up 16.3 becomes 17.
4 The Math object’s round() methods round 16.3 up only if the decimal part of the
number is 5 or higher (see Figure 9.25)
Figure 9.25 Output from Example 9.21.
Trang 6(such as for lotteries or card games) There are examples throughout this text where
ran-dom numbers are used
The Math object’s random() method returns a random fractional number between 0
and 1 and is seeded with the computer’s system time (The seed is the starting number
for the algorithm that produces the random number.) The Math object’s floor() method
truncates numbers after the decimal point and returns an integer
A wrapper is an object bearing the same name as the primitive data type it represents
For each of the primitive data types (string, number, and Boolean), there is a String
object, a Number object, and a Boolean object These objects are called wrappers and
E X A M P L E 9 2 2
<html>
<head><title>Random Numbers</title></head>
<body bgcolor="darkblue">
<p style="font-size:120%;color:white">
<script type="text/javascript">
1 for(i=0; i < 10;i++){
// Generate random numbers between 0 and 1
2 document.write(Math.random(),"<br />");
} document.write("<br />");
// Generate random numbers between 0 and 10
3 for(i=0; i < 20; i++){
4 document.write(Math.floor(Math.random() * 10 ) +" ");
}
</script>
</p>
</body>
</html>
E X P L A N A T I O N
1 The for loop is entered and will cause the body of the block to be executed 10
times, thus producing 10 fractional random numbers between 0 and 1
2 The random() method of the Math object produces random numbers between 0
and 1
3, 4 This for loop will cycle 20 times producing 20 random numbers between 0 and
10, achieved by multiplying the return value of the random number by 10 and
then using the floor() method to round down the number to produce a whole
number This will produce 0 but never 10 (see Figure 9.26 on page 247)
Trang 7provide properties and methods that can be defined for the object For example, the
String object has a number of methods that let you change the font color, size, and style
of a string; and the Number object has methods that allow you to format a number to a
specified number of significant digits Whether you use the object or literal notation to
create a string, number, or Boolean, JavaScript handles the internal conversion between
the types The real advantage to the wrapper object is its ability to apply and extend
properties and methods to the object, which in turn, will affect the primitive
We have used strings throughout this book They were sent as arguments to the write()
and writeln() methods, they have been assigned to variables, they have been
concate-nated, and so on As you might recall, a string is a sequence of characters enclosed in
either double or single quotes The String object (starting with JavaScript 1.1) is a core
JavaScript object that allows you to treat strings as objects The String object is also
called a wrapper object because it wraps itself around a string primitive, allowing you to
apply a number of properties and methods to it
You can create a String object implicitly by assigning a quoted string of text to a
vari-able, called a string primitive (see “Primitive Data Types” on page 53 of Chapter 3, “The
Building Blocks: Data Types, Literals, and Variables”), or by explicitly creating a String
object with the new keyword and the String() object constructor method Either way, the
properties and methods of the String object can be applied to the new string variable.
Figure 9.26 Producing random numbers (Example 9.22).