📓1.11: Math Class

Table of Contents

📖 This page is a condensed version of CSAwesome Topic 1.11

Using the Math Class

Games would be boring if the same thing happened each time you played the game. Random numbers can be used in games to generate different outcomes each time the game is played. In Java, the Math.random() method is used to generate a random number.

There are lots of mathematical methods in the Math class that you might want to use in your programs, like Math.pow(2,3) which calculates 2 to the power of 3, which is 8.

The Math class is part of the java.lang package. Classes in the java.lang package are available by default. The Math methods are class (static) methods which means you can call them by just using ClassName.methodName().

Mathematical Functions

The Math class contains the following methods that are in the AP CSA subset. There are many more Math methods, outside of what you need on the AP exam, that you can find in the Math class Javadocs.

Method Output
int abs(int) Returns the absolute value of an int value (which is the value of a number without its sign, for example Math.abs(-4) = 4)
double abs(double) Returns the absolute value of a double value
double pow(double, double) Returns the value of the first parameter raised to the power of the second parameter
double sqrt(double) Returns the positive square root of a double value
double random() Returns a random double value greater than or equal to 0.0 and less than 1.0 (not inclusive!)

All the Math methods that you may need to use or understand on the AP exam are listed in the AP CSA Reference Sheet that you can use during the exam.

These Math methods are mathematical functions that compute new values from their arguments.

Absolute Value

Math.abs takes a single argument, either a double or an int and returns a value of the same type which is the absolute value of the argument. The absolute value is the positive value of the number without its sign or its distance from 0.

Math.abs(45);    // returns 45
Math.abs(-45);   // returns 45
Math.abs(33.3);  // returns 33.3
Math.abs(-33.3); // returns 33.3

Exponentiation

Math.pow takes two argument, both doubles and returns a double which is the first argument raised to the power of the second argument.

Math.pow(2 , 3); // returns 8.0
Math.pow(10, 6); // returns 1000000.0
Math.pow(2, -3); // returns 0.125

Square Root

Math.sqrt takes an double argument and returns a positive double value which is the square root of the argument.

For example, the square root of 9 is 3 because 3 squared is 9.

Math.sqrt(9); // returns 3.0

Since these methods calculate and return a value, you need to use that value, for example in an assignment statement or in a print statement to see the result.

For example:

System.out.println("The square root of 9 is " + Math.sqrt(9));

Random Numbers

🎲 The Math.random() method returns a double number greater than or equal to 0.0, and less than 1.0.

When we talk about ranges of numbers, sometimes we need to be precise about whether the ends of the range are part of the range. When we need to be precise about this we’d say that it returns a number between 0, inclusive, and 1, exclusive, meaning include 0 but exclude 1. Lots of ranges in Java are expressed this way, as you’ll see later on with an inclusive bottom and exclusive top.

For example, Math.random returns a number between 0 and 1, but does that mean it can return exactly 0? Or exactly 1?

As it turns out, it can return 0.0, but never returns 1.0.

MANIPULATING THE RETURN VALUE

Getting a number between 0, inclusive, and 1, exclusive, may not seem all that useful. But we can expand the range easily enough by manipulating the output (adding, subtracing, multiplying or dividing the return value). And often we want a random integer, with nothing after the decimal point. Easy enough—casting a double to an int will throw away any values after the decimal point. For example:

    // rnd is an integer in the range 0-9 (from 0 up to 10).
    int rnd = (int)(Math.random()*10);

Finally, what if we want a number in a range that doesn’t start with 0, say a number from 1 to 10 (including 10) instead of from 0 to 9 (including 9)? Since the size of the two ranges is the same, with ten numbers in each, all we need to do is shift from the range we’ve generated into the range we want. In other words, add the difference between the two ranges, 1 in this case.

    // rnd is an integer in the range 1-10 (including 10).
    int rnd = (int)(Math.random()*10) + 1;
  • Math.random() returns a random number between 0.0-0.99.
  • (int)(Math.random()*range) + min moves the random number into a range starting from a minimum number.
  • The range of possible values is: (max - min + 1).

Here are some examples that move a random number into a specific range.

// Math.random() returns a random number between 0.0-0.99.
double rnd = Math.random();

// rnd1 is an integer in the range 0-9 (including 9).
int rnd1 = (int)(Math.random()*10);

// rnd2 is in the range 1-10 (including 10). The parentheses are necessary!
int rnd2 = (int)(Math.random()*10) + 1;

// rnd3 is in the range 5-10 (including 10). The range is 10-5+1 = 6.
int rnd3 = (int)(Math.random()*6) + 5;

// rnd4 is in the range -10 up to 9 (including 9). The range is doubled (9 - -10 + 1 = 20) and the minimum is -10.
int rnd4 = (int)(Math.random()*20) - 10;

So the general recipe for generating a random is to first stretch the value from Math.random() until it’s in the right size range by multiplying by the size of the range. Then if you want an integer value, cast to int to discard the part after the decimal point. Then shift the value up by adding the minimum value.

Summary

  • (AP 1.11.A.1) The Math class is part of the java.lang package. Classes in the java.lang package are available by default.

  • (AP 1.11.A.2) The Math class contains only class (static) methods. They can be called using Math.method(); for each method.

  • (AP 1.11.A.2) The following static Math methods are part of the Java Quick Reference:

    • int abs(int) : Returns the absolute value of an int value (which means no negatives).
    • double abs(double) : Returns the absolute value of a double value.
    • double pow(double, double) : Returns the value of the first parameter raised to the power of the second parameter.
    • double sqrt(double) : Returns the positive square root of a double value.
    • double random() : Returns a double value greater than or equal to 0.0 and less than 1.0 (not including 1.0)!

  • (AP 1.11.A.3) The values returned from Math.random() can be manipulated to produce a random int or double in a defined range.

  • (int)(Math.random() * range) + min moves the random number into a range starting from a minimum number. The range is the (max - min + 1). For example, to get a number in the range of 5 to 10, use the range 10-5+1 = 6 and the min number 5: (int)(Math.random()*6) + 5.

Acknowledgement

Content on this page is adapted from Runestone Academy - Barb Ericson, Beryl Hoffman, Peter Seibel.