Unit 1.11: Using the Math Class¶

Scope: CS Awesome 2, Section 1.11

Learning Goals¶

By the end of this lesson, you should be able to:

Call class methods in Math.
Use abs, pow, sqrt, and random.
Select the correct overloaded abs method.
Generate random values in a requested range.
Avoid common casting and range errors.

The `Math` Class¶

Math belongs to java.lang, so no import is required. Its methods are class methods and are called with the class name and dot operator.

double root = Math.sqrt(81.0);

Do not create a Math object. Use Math.method(arguments).

AP Java Quick Reference Methods¶

Method	Return value
`int abs(int x)`	absolute value of an `int`
`double abs(double x)`	absolute value of a `double`
`double pow(double base, double exponent)`	base raised to exponent
`double sqrt(double x)`	positive square root
`double random()`	random `double` in `[0.0, 1.0)`

Absolute Value¶

abs is overloaded. Argument type determines which version is called.

int distance1 = Math.abs(-12);       // 12
double distance2 = Math.abs(-3.75);  // 3.75

The return type matches the selected overload.

int a = Math.abs(-4);       // valid
double b = Math.abs(-4.0);  // valid
int c = Math.abs(-4.0);     // invalid: double result into int

Powers and Square Roots¶

double square = Math.pow(5, 2); // 25.0
double cube = Math.pow(2, 3);   // 8.0
double root = Math.sqrt(49);    // 7.0

Both pow and sqrt return double, even when their arguments and mathematical results look like whole numbers.

Pythagorean distance:

double width = 6.0;
double height = 8.0;
double diagonal = Math.sqrt(Math.pow(width, 2) + Math.pow(height, 2));
System.out.println(diagonal); // 10.0

Random Numbers¶

double value = Math.random();

The result satisfies:

0.0 <= value < 1.0

1.0 is excluded.

Random Integer from Zero¶

To generate one of 0, 1, 2, 3, 4:

int value = (int) (Math.random() * 5);

Scale first, then cast. Casting Math.random() before multiplication always produces 0.

int wrong = (int) Math.random() * 5; // always 0

Random Integer in an Inclusive Range¶

For an integer from min through max, inclusive:

int value = (int) (Math.random() * (max - min + 1)) + min;

For 5 through 10:

int value = (int) (Math.random() * 6) + 5;

Possible pre-cast values are from 0.0 up to but not including 6.0; the cast yields 0 through 5, and adding 5 gives 5 through 10.

Random Double in a Range¶

For a double from min inclusive to max exclusive:

double value = Math.random() * (max - min) + min;

Practice Missions¶

Mission 1: Method and Type Trace¶

Predict the value and type of each expression:

Math.abs(-9)
Math.abs(-9.0)
Math.pow(3, 2)
Math.sqrt(2.25)

Mission 2: Coordinate Distance¶

Given two points (x1, y1) and (x2, y2), write an expression for the straight-line distance using Math.pow and Math.sqrt.

Mission 3: Random Locker¶

Write expressions for:

an integer from 0 through 7;
an integer from 12 through 20;
a double from -2.0 inclusive to 3.0 exclusive.

For each, prove the minimum and maximum possible result.

Mission 4: Repair the Random Formula¶

The code is intended to produce an integer from 1 through 6, but always prints 1. Explain and fix it.

int die = (int) Math.random() * 6 + 1;

Mission 5: Nested Methods¶

Write one expression that calculates the absolute difference between Math.sqrt(80) and 9. Store the result in a correctly typed variable.

Key Summary¶

Concept	Core idea
`Math`	`java.lang` class containing class methods.
`abs`	Overloaded for `int` and `double`.
`pow`	Returns a `double` power.
`sqrt`	Returns a positive `double` square root.
`random`	Returns a value in `[0.0, 1.0)`.
Inclusive integer range	`(int)(Math.random() * range) + min`.

Source scope: CS Awesome 2, Unit 1.11