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., ?, e, Planck's constant, the atomic weight of molybdenum, the boiling point of water in degrees Kelvin, whatever you like. Call this constant ?. Then select any four positive 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 w^ax^by^cz^d, where each of a, b, c, and d is 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 ? 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: ? = 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; also the record for wins in a year by any college team), 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^-5102329¹1936^1/213⁴ is about 239,103, which is within about 0.08% of ?.

Your job is to create a Java program that asks the user what constant ? 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 exponentsa,b, c, and d that bring the de Jager formula as close as possible to ?, as well as the value of the formula w^ax^by^cz^d and the relative error of the approximation to the nearest hundredth of one percent.

Edit your java program to satisfy the problem requirements stated above, as well as the following additional requirement: use only while loops for iteration.

Any help on this is appreciated. I am having a hard time even starting it.