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/* The reason I created this was two-fold.  1. To learn Java 2. To learn about numerical analysis and numerical methods of arithmetic. 
This code shows that the Babylonian Method of computing square roots is as accurate as the Java numerical method using sqrt() after as few
as 10 iterations for numbers within the limits of a double.  I'm certain that it can be improved (and I have no vanity of authorship i.e., I welcome
criticism  aaron.paul.clark@gmail.com).  I love learning and sharing what I find, if you have some math-related code you're itching to share please
let me know!

There are numerous methods for computing square roots (http://en.wikipedia.org/wiki/Methods_of_computing_square_roots). 
"The basic idea is that if x is an overestimate to the square root of a non-negative real number S then S/x will be an underestimate and so the average 
of these two numbers may reasonably be expected to provide a better approximation."

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/* The reason I created this was two-fold.  1. To learn Java 2. To learn about numerical analysis and numerical methods of arithmetic. 
This code shows that the Babylonian Method of computing square roots is as accurate as the Java numerical method using sqrt() after as few
as 10 iterations for numbers within the limits of a double.  I'm certain that it can be improved (and I have no vanity of authorship i.e., I welcome
criticism  aaron.paul.clark@gmail.com).  I love learning and sharing what I find, if you have some math-related code you're itching to share please
let me know!

There are numerous methods for computing square roots (http://en.wikipedia.org/wiki/Methods_of_computing_square_roots). 
"The basic idea is that if x is an overestimate to the square root of a non-negative real number S then S/x will be an underestimate and so the average 
of these two numbers may reasonably be expected to provide a better approximation."

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import javax.swing.JOptionPane;
import java.io.*;
import static java.lang.Math.*;
public class BabylonianSqrt6 {
	public static void main(String[] args) {
	
	String S;
	S = JOptionPane.showInputDialog(null, "Enter a Whole Integer");
	
	int SigFigs = 0;

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!
! Last configuration change at 22:42:44 UTC Thu Jun 7 2012 by joe
upgrade fpd auto
version 15.1
service timestamps debug datetime msec
service timestamps log datetime msec
service password-encryption
!
hostname cisco1

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/***********************************************
* HelloGUI.java
* Aaron P. Clark
*
* One of the last programs of the chapter.  Exhibits
* the use of the JOPtionPane GUI
***********************************************/

import javax.swing.JOptionPane;
public class HelloGUI

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/***********************************************
* CirclePrompt.java
* Aaron P. Clark
*
* Created to understand java.util.Scanner and Ch 2. 
* shows the area of a circle if you say it's your
* favorite shape when prompted.  See P.32 in our
* text for the pseudocode
***********************************************/

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/***********************************************
* HappyBirthday.java
* Aaron P. Clark
*
* Based on the pseudocode while loop on p.37 in Ch 2. 
* prints "Happy birthday!" 100x
***********************************************/

public class HappyBirthday 
{

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/***********************************************
* printLoop.java
* Aaron P. Clark
*
* Created from pseudocode in Ch. 2 of Park Univ.
* book.  I wanted to figure out how to print something
* a given number of times.
***********************************************/

// Created from pseudocode in Ch. 2 of Park University book.  

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/***********************************************
* whileLoop.java
* Aaron P. Clark
*
* I created this for Park programming calss to learn
* how to accept command-line input in a loop
***********************************************/
import java.util.Scanner;  
 
public class whileLoop

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/***********************************************
* WhileLoopSentinalValue.java
* Aaron P. Clark
*
* Based on the pseudocode while loop on p.40 in Ch 2. 
* Takes scores and computes average.  
***********************************************/
 
import java.util.Scanner;