Objectives

1. Familiarity with using wh ile loops and static methods

2. Exposure to using nested wh ile and for loops and arrays

The Problem

In his book Irreligion, the mathematician John Allen Paulos tells an amusing story about the Dutch astronomer Cornelis de      Jager, "who concocted the following algorithm for personalized physical constants, [and] used it to advance a charming          theory about the metaphysical properties of Dutch bicycles." First select any positive real-valued universal physical or              mathematical constant that seems interesting to you, e.g., π, e, Planck's constant, the atomic weight of molybdenum, the        boiling point of water in Kelvin, whatever you like. Call this constant μ . Then select any four positive real numbers not equal to 1 that have personal meaning to you, e.g., your favorite number, day or month or year of birth, age in fortnights or seconds,   weight in stones or grams, height in furlongs or millimeters, number of children, house number, apartment number, zip code, last four digits of SSN, whatever you like. Call these four personal numbers w, x, y, and z.

Now consider the de Jager formula waxbyczd, where each of a, b, c, and dis one of the 17 numbers {-5, -4, -3, -2, -1, -1/2,        -1/3, -1/4, 0, 1/4, 1/3, 1/2, 1, 2, 3, 4, 5}. The "charming theory" asserts that the de Jager formula with your four personal          numbers can be used to approximate μ within a fraction of 1% relative error. For example, suppose you choose to                    approximate the mean distance from the earth to the moon in miles: μ = 238,900. And suppose you are an OSU sports fan, so your personal numbers are the number of wins in OSU's last national championship season (14), the seating capacity of Ohio  Stadium (102,329), the year of Jesse Owens' four gold medals in Berlin (1936), and your jersey number when you played high school field hockey (13). Then the value of 14-5 1023291 19361/2 134 is about 239,103, which is within about 0.08% of μ .

Your job is to create a Java program that asks the user what constant μ should be approximated, and then asks in turn for       each of the four personal numbers w, x, y, and z. The program should then calculate and report the values of the exponents a, b,  the         relative error of the approximation to the nearest hundredth of one percent (see SimpleWriter print(double, int, boolean) for a     method you may find useful for this). Note that your program must find the combination of exponents that minimizes the error of the approximation of μ and then print the exponents, best approximation, and corresponding relative error.      (Essentially this program could be used to disprove the "charming theory" by finding μ, w, x, y, and zsuch that the best approximation of μ results in a relative error that is greater than 1%.)

Method

1. Create a new Eclipse project by copying ProjectTemplate or a previous project you have created, naming the new project Pseudoscience. In the src folder of this project and the default package, create a class called ABCDGuesser1.

2. Edit ABCDGuesser1.java to satisfy the problem requirements stated above, as well as the following additional requirements:   Use only wh ile loops for iteration.

  Check that the inputs provided by the user are valid, i.e., the input for μ is a positive real value and the inputs for w,

x, y, and zare each a positive real value not equal to 1. You should implement and use two new static methods declared as follows: