All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math > Calculus
The Almost Pythagorean Theorem (Posted on 2017-02-03) Difficulty: 3 of 5
A pretty good approximation of the Pythagorean Theorem to find the hypotenuse of a right triangle is to add the length of the longer leg to half the length of the shorter leg.

For what ratio of leg lengths is this approximation worst? How bad is it?

No Solution Yet Submitted by Jer    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Solution only. Comment 1 of 1

The worst approximation occurs when the long leg is twice the length of the short. At that point, the error is as sqrt(5)/2  is to 1.

When the long leg is almost as long as the hypotenuse, the shorter leg more or less falls out of the picture and the approximation becomes increasingly accurate.

To complete the picture, when the legs are equal, the error is as 3/(2sqrt(2)) is to 1.


  Posted by broll on 2017-02-04 00:10:45
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information