Showing posts with label Math. Show all posts
Showing posts with label Math. Show all posts

Friday, May 13, 2005

Fighting the Future, One Square Root at a time

Find the square root for Y
Stage One:
1. Determine the largest squared whole number less than Y.
2. Use the square root of the largest squared whole number to be the first part of the answer. Place this number to the left of the decimal place within the answer.
3. Find the difference of Y and the squared whole number.

Stage Two:
1. Multiple the difference by 100, designated as A.
2. Multiple the answer so far by 2 (without the decimal point), designated as B.
3. Multiple B by 10.
4. Give C one of the following values: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
5. Find D where (B+C)*C equals the greatest value less than A.
6. C becomes the next digit right of the decimal in the answer.
7. Find the difference between of A and D.
8. Repeat Stage Two until the answer reaches the desired number of digits after the decimal.


PDF File: Example to find the square root of 3

(Sorry, I had to make it a PDF file because html isn't good at showing math equations and I didn't want to scan in my chicken scratch writing. Free Acrobat Reader is a must, but if you don't already have it, go here to get it:

Now, is anyone ever going to use this? Hey, if anyone has seen this method in print, please let me know.

Tuesday, May 10, 2005

Preface to Square Root

Back when I was in high school, I learned something that isn’t known by very many people. I learned the method to manually find a square root in a way that is similar to long division. This method allows you to find each decimal place with certainty. You can solve to as many places after the decimal point as you want.
I've never found this long method in print anywhere. I’ve found other simpler methods to finding a square root, but they usually involve closing in on the square root by continuously rerunning the same method. You are never left with a perfect answer because you can never be sure if the successive decimal places are correct. I’m also not sure which method is used by calculators (on which we all depend for square roots these days, which is the beginning of Asimov’s vision for our world coming true, but that’s a future blog entry).
I have no clue why this long method works. But, in a very small effort to fight the future, I’m going to show the method here, soon.

UPDATE: Here's the link to the long method of finding square roots: