Assignment 1 Average.java

CS2133: Computer Science II
Assignment 1

1 Not Hello World (10 points)
This problem will ensure that your programming environment is functional and you remember how
to compile a simple Java class. Write a program called Greeting.java that prints out a greeting. It
can say anything you like, except for “Hello, world!”
$ java Greeting
Bonjour, tout le monde!
2 Statistics (30 points)
Write a program called Average.java that prompts a user to enter a number, and allows the user to
continue to enter numbers until she responds with a negative number. At that point, the program
should print out how many numbers the user entered (not including the negative one), and the
average of those numbers. Note: This program will use a Scanner object such as you learned about
in CS I. This is the only occasion in this class that you are likely to use a Scanner object for user
interaction. You will be using command-line arguments or GUI widgets in every other program
you write (or, sometimes, not interacting with a user at all).
$ java Average
Enter a series of numbers. Enter a negative number to quit.
1
2
4.5
3
5
-1
You entered 5 numbers averaging 3.1.
3 Fibonacci numbers (30 points)
The Fibonacci sequence is a famous mathematical sequence where each successive term is the sum
of the two preceding ones. This can be expressed mathematically as Fn = Fn−1 + Fn−2, where
F1 = 1 and F2 = 1. The sequence, therefore, goes 1, 1, 2 (1+1), 3 (1+2), 5 (2+3), 8 (3+5),
13 (5+8), 21, 34, 55, 89, 144... Write a program called Fib.java which allows a user to enter a
1
number n as a command-line argument. The program will print out the nth Fibonacci number.
Hint: you will have to change the argument in the variable arg[0] from a String to an int using
Integer.parseInt().
$ java Fib 4
3
$ java Fib 7
13
$ java Fib 11
89
4 Investigations into π (30 points)
Thirty-five digits of π are sufficient to calculate the circumference of the universe to within the size
of a hydrogen nucleus. In other words, finding the value of π to ten quadrillion digits is pretty
much the definition of pointless. But people seem to enjoy doing it anyhow. How? There are a
number of methods, but one common approach is to discover an infinite series that converges to
the correct value. Here’s one that has been around for hundreds of years, known as the Gregory
series:
π
4 =
P∞
k=1
(−1)k+1
2k−1 = 1 −
1
3 +
1
5 −
1
7 + · · ·
Write a program called Gregory.java that takes a number n specified by the user (via the
command line) and calculates π using the first n terms of the Gregory series. The program should
print this approximate value of π, as well as the percentage error between this value and the one
provided by Java in the constant Math.PI. Hint: remember to correct for the fact that this series
converges to π
4
, not π itself.
$ java Gregory 10
Pi according to Gregory series: 3.0418396189294032
This differs from Java’s value by 3.175237710923643 percent.
$ java Gregory 1000
Pi according to Gregory series: 3.140592653839794
This differs from Java’s value by 0.03183098066059948 percent.
Turning in
Ensure that all four of your .java programs can be compiled and run from the command line.