At the end of a recent post, Phi Furthermore, 1/3/2013, I was remarking on how one gets different answers to calculations, depending on how many decimal places one uses. My calculator only has 8 digits, so my work is limited.
I emailed a real mathematician who understands Fibonacci Series and he most kindly replied.
I am very grateful for it has opened up a new way for me.
Here is part of his reply:-
My Phi to the power 36 was 33385270 and this is close, but not exact.
maybe I should write "33385270........." to be more honest.
For my own purposes it is ok to be not too exact for one can see Patterns and Equations to show Rules or Trends. I am glad to offer these distinctions in the interests of better reporting.
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This is more advice for me to work with. This is the second time a mathematician has mentioned the Lucas Series to me, but only now do I understand.
If Phi to the power 36 is 33385281.9999999700466810494516.....
then Phi to the power minus 36 , ie 1 / Phi to power 36 =
0.0000000299533189505483553
using the Scientific Calculator.
Adding them together = 33385282****
Actually it is embarrassingly a mistake!
7/7/2013 I am checking the numbers
add together = 3385281.9999999999999999999999553
which is not the nearest integer! but almost.
= A whole new world?
7/7/2013-------oh dear, it was not so magic after all.
I am studying the various values of Phi in the future posts "Refinding Phi"
Regarding the calculator- it seems sometimes answers are "rounded off"
eg a previous result for Phi to power -36
=..........with 189505484 at the end.
Plus in the first calculation I missed out the 7 in the Phi to power 36 number.
It goes to show that results are only as good as the human operator!
My thanks the the mathematician who gave me good advice.
I welcome comments anytime, especially if I have made some mistake, (which often happens).
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I searched online for Mathematica or similar to enable me to do long calculations.
I founs it to be a software program from Wolfram Maths, and it costs more than $100.
A cheaper one was Math Studio which I purchased for $30. When I looked into it, yikes it was forbiddingly complicated! More difficult than my first year university maths in 1966!
I clicked on fibonacci - and foiled already!- "file unknown". All I wanted was a better calculator.
Next try was looking for an online calculator and I found a Free one.
http://web2.0calc.com This is a Scientific Calculator and it works to 50 digits or so.
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There is more story.......... When I looked for www.mathstudio.net I was WARNED security problem with this site! I felt a bit cheated and worried.
I tried http://www.mathstudio.net and this one was OK.
(PS. 10/5/2013 The professional computer repairers at Propellerhead fixed it for me,
icon, maths file and all. Thanks, guys.)
It was a big lesson for me.
All the online references I quote in my blogs should have http:// in front of them for the security of my readers!
Yikes--- what a big job if I have to go and correct all my work! Plus correcting all my numbers.
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It has been a long hot and dry Summer in my caravan without electricity. Hardly any rain. Not much luck growing vegetables. Hardly any bees. Fire! 8 km away, twice, east and south. I will post photos in my other blog asap. Autumn is bringing kinder days and hopefully a Happy Easter.
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