My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree1Thanks
Reply
 
LinkBack Thread Tools Display Modes
February 7th, 2015, 10:46 AM   #1
Newbie
 
Joined: Feb 2015
From: England

Posts: 1
Thanks: 0

Trial and Improvement Equation

Hallo,
My friend who is from a foreign country never heard of the little GCSE practice we call Trial and Improvement, he thinks its useless and not mathematical. (as it is just guessing and could not provide a correct answer) He claims there would be a different way to answer all trial and improvement equation,

Can anyone think of one equation that only can be solved using the trial and improvement method? I am genially now questing the usefulness of this method on the other had would be sweet to prove him wrong.
Skorpi007 is offline  
 
February 7th, 2015, 10:56 AM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,502
Thanks: 2511

Math Focus: Mainly analysis and algebra
There are other methods and they are generally better, but none is as simple to understand as trial and improvement. There are probably no problems that can only be solved in this way, but it is a good introduction to the concept of approximating solutions.

Having said that, the iteration $$a_{n+1} = \frac12 \left(a_n + {b \over a_n}\right)$$
is just about the most efficient approximator for $\sqrt b$ and uses basically the same idea. It was used by the Babylonians around 2000 years ago.

Last edited by v8archie; February 7th, 2015 at 11:06 AM.
v8archie is offline  
February 7th, 2015, 12:05 PM   #3
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,459
Thanks: 949

Archie, help please...
I can tell (by quoting your post) that you used this:
$$a_{n+1} = \frac12 \left(a_n + {b \over a_n}\right)$$

However, [Math Processing Error] in red ink appears where the result of above
should appear; do you have any idea what's wrong with my computer:
like, Java not updated or whatever?

I see that someone else brought up something similar:
Math Error

Thanks for any help, suggestions, ....

Last edited by Denis; February 7th, 2015 at 12:09 PM.
Denis is offline  
February 7th, 2015, 12:10 PM   #4
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,502
Thanks: 2511

Math Focus: Mainly analysis and algebra
Try refreshing the page. It's all JavaScript, not Java.
v8archie is offline  
February 7th, 2015, 12:23 PM   #5
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,459
Thanks: 949

Refreshing does nothing!!

To perhaps clarify further, this is what I "see" when looking at your post:

There are other methods and they are generally better, but none is as simple to understand as trial and improvement. There are probably no problems that can only be solved in this way, but it is a good introduction to the concept of approximating solutions.

Having said that, the iteration [Math Processing Error]is just about the most efficient approximator for [Math Processing Error] and uses basically the same idea. It was used by the Babylonians around 2000 years ago.

Last edited by Denis; February 7th, 2015 at 12:26 PM.
Denis is offline  
February 7th, 2015, 12:33 PM   #6
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,502
Thanks: 2511

Math Focus: Mainly analysis and algebra
Try refreshing with SHIFT+F5 or clearing the browser cache. The page works fine for me.

Can you see this?
$$a_{n+1} = \frac12 \left( a_n + \frac{b}{a_n} \right)$$
v8archie is offline  
February 7th, 2015, 12:44 PM   #7
Senior Member
 
aurel5's Avatar
 
Joined: Apr 2014
From: Europa

Posts: 575
Thanks: 176

Quote:
Originally Posted by Skorpi007 View Post
would be a different way to answer all trial and improvement equation,

This is a tedious procedure.
Start by estimating the solution (you may be given this estimate).
Then substitute this into the equation to determine whether your estimate is too high or too low.
Refine your estimate and repeat the process.

Example

Solve t³ + t = 17 by trial and improvement.
Firstly, select a value of t to try in the equation. I have selected t = 2. Put this value into the equation. We are trying to get the answer of 17.
If t = 2, then t³ + t = 2³ + 2 = 10 . This is lower than 17, so we try a higher value for t.
If t = 2.5, t³ + t = 18.125 (too high)
If t = 2.4, t³ + t = 16.224 (too low)
If t = 2.45, t³ + t = 17.156 (too high)
If t = 2.44, t³ + t = 16.966 (too low)
If t = 2.445, t³ + t = 17.061 (too high)

We know that t is between 2.44 and 2.445.

So to 2 decimal places, t = 2.44.
aurel5 is offline  
February 7th, 2015, 12:48 PM   #8
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,459
Thanks: 949

No, can't see it.
And I know about the F5 "refresher"!
Plus I keep no history: automatic...

Well, I sure ain't alone:
http://meta.stats.stackexchange.com/...ocessing-error

Last edited by Denis; February 7th, 2015 at 12:54 PM.
Denis is offline  
February 7th, 2015, 01:23 PM   #9
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,502
Thanks: 2511

Math Focus: Mainly analysis and algebra
Well I only ever see that error when I get a slow connection and the JavaScript fails to load properly. I would still clear the cache (that's not the same as the history).
Thanks from Denis
v8archie is offline  
February 7th, 2015, 01:53 PM   #10
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,459
Thanks: 949

Thanks Archie.
Denis is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
equation, improvement, trial



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Trial and Improvement fliss1992 Algebra 6 May 6th, 2014 08:41 PM
Most efficient trial division algorithm using prime forms? Sebastian Garth Number Theory 15 December 24th, 2011 01:33 PM
stability improvement of equation system a_kamali Linear Algebra 0 August 15th, 2011 06:16 AM
improvement bentick Academic Guidance 2 November 1st, 2010 10:38 AM





Copyright © 2018 My Math Forum. All rights reserved.