# Is this a fix?

To find a fix-point function suitable for finding a square root, for instance of 2, we can begin with

t^2= 2

subtract the square of an integer from both sides (in this case 1) gives:

t^2-1=1

use the difference of two squares factorization on the left-hand-side to get

(t-1)(t+1)=1

divide by one of the factors on the left-hand-side giving (t-1)=1/(t+1)

and finally add 1 to both sides giving

t=1+1/(t+1)

i.e. the fix point function to use is fix(t)=1+1/(t+1).

Plot the graph of y(t)=t^2-2 and perform zero finding using fix(t). The value of t found should be the square root of 2.

Use the same method to find the square root of 5.

Can a similar method of rearrangement work for cube roots?

#sequences #equationsolving #numericalmethods

plotXpose app is available on Google Play

Google Play and the Google Play logo are trademarks of Google LLC.

Versions will shortly be available for iOS and Windows.

Google Play and the Google Play logo are trademarks of Google LLC.

Versions will shortly be available for iOS and Windows.

plotXpose app is a companion to the book Mathematics for Electrical Engineering and Computing by Mary Attenborough, published by Newnes, 2003.