Newton had a fun way to approximate general roots...
#5
That all looks a bit hard for me...
I've been using "successive approximation", which I suspect is just another way of doing the same thing but is easier (for me) to understand:

DefDbl R, I, N
root = 1: IncRate = 1
Input "Number"; number
While root * root <> number
root = root + IncRate
If prevroot = root Then Exit While
If root * root > number Then
root = root - IncRate
IncRate = .9 * IncRate
End If
Print IncRate;
prevroot = root
Wend
Print "Root is"; root
Sleep

Of course, this only works within the limits of Double. The prevroot bit is to stop it if the same root is given twice.
Of all the places on Earth, and all the planets in the Universe, I'd rather live here (Perth, W.A.) Big Grin
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RE: Newton had a fun way to approximate general roots... - by PhilOfPerth - 09-13-2022, 06:57 AM



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