Math Class & Common Algorithms

Objective #1: Use the Math class for routine mathematical tasks.

• The Math class is automatically imported with Java programs. It contains many useful methods and constants.
  
  
• You can use a number of Math class methods (i.e. static methods) such as the following methods that you should know for the AP exam or class tests:
  
  
  • Math.sqrt(x) - which obtains the square root of a value. Note that this method returns a double and not an int.
    
    int num = Math.sqrt(10);     and     int num = Math.sqrt(9);     cause errors since sqrt returns a double which cannot be assigned to an int even if the double is 3.0 for example.
    
    
  • Math.pow(x, y) - which is used to compute x to the yth power
    
    System.out.println(Math.pow(2, 8));    displays 256 which is 2 raised to the 8th power.
    
    
  • Math.abs(x) - to compute the absolute value of x
    
    
  • Math.max(x, y) - returns x or y, whichever is greater
    
    System.out.println(Math.max(-2, 3));   displays 3 since 3 is greater than -2
    System.out.println(Math.max(Math.max(1, 4), 2));    displays 4
    
    
  • Math.min(x, y) - returns x or y, whichever is least
    
    
  • Math.round(x) - to round x to the closest integer
    
    System.out.println(Math.round(4.5));   displays 5
    System.out.println(Math.round(4.4));   displays 4
    
    
    
  • Math.ceil(x) - to find the smallest integer that is greater than or equal to x. Note that this method returns a double so the statement      int num = Math.ceil(2.3);    causes a compile error.
    
    System.out.println(Math.ceil(3.1));     displays 4
    System.out.println(Math.ceil(-2.9));    displays -2
    
    
  • Math.floor(x) - to find the largest integer that is less than or equal to x. Note that this method returns a double so the statement      int num = Math.floor(2.3);    causes a compile error.
    
    System.out.println(Math.floor(3.9));     displays 3
    System.out.println(Math.floor(-2.1));    displays -3
    
    
  • Math.random() - returns a pseudorandom floating-point value greater than or equal to zero but less than 1; that is a value in the range [0, 1)
    
    You are not responsible for memorizing or using the methods below on the AP exam or class tests but they are convenient.
    
    
  • Math.sin(x) - to compute the sine of x in radians
  • Math.cos(x) - to compute the cosine of x in radians
  • Math.tan(x) - to compute the tangent of x in radians
  • Math.toRadians(x) - to convert x radians to degrees (i.e. returns x * 180/Math.PI)
  • Math.toDegrees(x) - to convert x degrees to radians (i.e. returnx x * Math.PI/180)
  • Math.exp(x) - to compute e to the xth power
  • Math.log(x) - to compute the natural log of x (i.e. ln(x) where x > 0)
    
    
• The methods above are called static methods. You do not need to instantiate a Math object in order to use the methods. You simply type the name of the class Math followed by a dot operator and then the name of the method.
  
  
• You can use a reasonably good approximation of pi by referencing the constant Math.PI in a Java program. You can use Euler's constant, e, by referencing the constant Math.E.
  
  For example, the following code could be used to display the area of a circle that has a radius of 5 units
  
  int radius = 5;
  System.out.println(Math.PI * Math.pow(radius, 2));
  
  

Objective #2: Use handy mathematical algorithms with casting and Math class methods.

• To truncate (or "chop off") the decimal part of a decimal number you can cast the double to an int:
  
  double num = 123.456;
  System.out.println((int) num); // 123
  
  
• To extract the digits in the decimal part of a decimal number:
  
  double num = 123.456;
  System.out.println(num - (int) num); // 0.456
  
  
• To find the maximum integer out of 3 numbers without using an if statement:
  
  int x = 3, y = 4, z = 2;
  System.out.println(Math.max(Math.max(x, y), z)); // 4
  
  
• To convert a number to a String by concatenating an empty string to an int
  
  int numberZip = 19610;
  String stringZipCode = numberZip + ""; // "19610"
  
  
• To convert a String to an int
  
  String stringZipCode = "19610";
  int numberZipCode = Integer.parseInt(stringZipCode); // 19610
  
  
• To convert a String to a double
  
  String stringPrice = "19.99";
  double numberPrice = Double.parseDouble(stringPrice); // 19.99
  
  
• To round a decimal number to the nearest whole number by casting:
  
  double unrounded = 12.56789;
  System.out.println( (int) (unrounded + 0.5)); // 13
  
  or, using an available Math class method
  
  double unrounded = 12.56789;
  System.out.println( Math.round(unrounded)); // 13
  
  
• To round a decimal number to the nearest tenth's place by casting:
  
  double unrounded = 12.56789;
  System.out.println( (int) (unrounded * 10 + 0.5) / 10.0); // 12.6
  
  
• To round a decimal number to the nearest hundredth's place by casting:
  
  double unrounded = 12.56789;
  System.out.println( (int) (unrounded * 100 + 0.5) / 100.0); // 12.57