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The Math Class
While the Math class is quite extensive, we will limit our attention to the
 methods listed below for the time being.

Method Purpose
abs(int x) Returns the absolute value of an integer x.
abs(double x) Returns the absolute value of a double x
pow(double base, double exponent) Returns the base raised to the exponent.
round(double x) Returns x rounded to the nearest whole number.  Returned value must be cast to an int before assignment to an int variable.
max(int a, int b) Returns the greater of a and b.
min(int a, int b) Returns the lesser of a and b.
double sqrt(double x) Returns the square root of x.
random( ) Returns a random number greater than or equal to 0.0 and less than 1.0.

These methods are used by invoking the name of the class (Math), followed by a dot (.), followed by the name of the method and any needed parameters.

SYNTAX:    radius = Math.sqrt(area/Math.PI));

 

More Examples:
int ans1;
double ans2;
ans1 = Math.abs(-4);            //ans1 equals 4
ans1 = Math.abs(-3.6);         //ans1 equals 3.6

ans2 = Math.pow(2.0,3.0);   //ans2 equals 8.0
ans2 = Math.pow(25.0, 0.5);  //ans2 equals 5.0

ans1 = Math.max(30,50);        //ans1 equals 50
ans1 = Math.min(30,50);        //ans1 equals 30
ans1 = (int) Math.round(5.66);   //ans1 equals 6


Random Number Generation
 
Computers can be used to simulate the generation of random numbers with the use of the random( ) method.  This random generation is referred to as a pseudo-random generation.  These created values are not truly "random" because a seeded mathematical formula is used to generate the values.

Remember that the random( ) method will return a value greater than or equal to zero and less than 1.  But don't expect values necessarily like .5 or .25.  The following line of code:
double randomNumber = Math.random( );
will most likely generate a number such as 0.7342789374658514.  Yeek!

When you think of random numbers for a game or an activity, you are probably thinking of random "integers".  Let's do a little adjusting to the random( ) method to see if we can create random integers.

Generating random integers within a specified range:

In order to produce random "integer" values within a specified range, you need to manipulate the random( ) method. 
 Obviously, we will need to cast our value to force it to become an integer.
The formula is:

int number = (int) (a + Math.random( ) * (b - a + 1));

a = the first number in your range
b = the last number in your range
(b - a + 1 ) is the number of terms in your range.
(range computed by  largest value - smallest value + 1)

Examples:
     random integers in the interval from 1 to 10 inclusive.

                    int number = (int) (1 + Math.random( ) * 10);

     random integers in the interval from 22 to 54 inclusive.
                    int number = (int) (1 + Math.random( ) * 33);
        
note:  the number of possible integers from 22 to 54 inclusive is 33
                             b - a + 1  =  54 - 22 + 1  =  33

                                 
 

                     
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