Yes, please post the solution.

I have a niggling feeling I am missing a clue re the “rational numbers” thing.

John_Taverner wrote on Sep 6^th, 2022 at 10:33am:


In foxholes nobody is cooking with microwaves.

OK, here is the solution:

a = 41/12
b = 49/12
c =  31/12


This is the very crude method  I used:

I set up a spreadsheet with a row from 1 to 1000.
in the second row I used (A1/12)^2 and filled up to 1000
In the third row, I used B 1+5 and filled
In the fourth row, I used B1+10 and filled

Then in row 5 and 6, I used something like:
=IF(ISERROR(MATCH(C1,B:B, 0)), "", "Match on row " & MATCH(A1,B:B, 0))

I also used conditional formatting to colour it red.

So, I'm looking for instances where B1+ 5 and B1+10 both exist in the row.

I could also have used nested loops to do the same thing using a small BASIC program.

Fibonacci must have had a more elegant mathematical way of getting to the solution though.

To get the spreadsheet to work, I had to multiply the values by the square of the denominator first to obtain whole numbers. Spreadsheets find it difficult to compare infinitely repeating numbers.

I have an incredible respect for these Renaissance mathematicians.

John_Taverner wrote on Sep 10^th, 2022 at 9:07pm:



That's not a mathematical solution -
it's an iterative solution.
I suspected it was a trick question.


Bobby,
Quote:



Also - polynomials normally have complex roots.
They are seen in a mathematical solution.

Frank wrote on Sep 11^th, 2022 at 7:06pm:


In this case, if you substitute the values given into the original equations, blind Freddy can see that the solution is valid. It’s about as mystical as a lump of cheese.

However, I think along the same lines as the quotation (apart from the claiming territory crap) and I agree that there is a spark of the divine in mathematics. In a basic sense, that “divine” equates with intelligent life. Whether you actually call it divine or otherwise is not really relevant. As soon as you define something with a word, the word itself changes the nature of that something:

If you represent existence with a totally calm, totally clear pond and you throw a small pebble into that pond, you create ripples which make the pond easier to discern, but changes the nature of the pond. That pebble is the word and the person who threw it, the observer.

Going further, the universe has an innately complex mathematical foundation. Is it a “divine” foundation? Whatever you call it, it’s beautiful and awe inspiring.

( and yes, I get up early. It’s part of growing old)

John_Taverner wrote on Sep 12^th, 2022 at 4:47am:



Nevertheless - if you don't understand what I wrote
then you're a mathematical dunce.

John_Taverner wrote on Sep 12^th, 2022 at 5:10am:


So who are YOU calling 'old man', then?

"By the way, logarithmically you are half way between the Universe and an atom."
(40 mins 20 secs.)



Dawkins's argument is that if HE were god he wouldn't do it this way.

John_Taverner wrote on Sep 17^th, 2022 at 6:00pm:



Lennox is after my own heart although my convictions are a lot weaker than his. He does make it clear, as does Dawkins despite himself, that god is NOT a scientific question (like so many other, lesser things aren't).


https://www.youtube.com/watch?v=OVEuQg_Mglw
55.20 esp 55.55

It is a delight to to listen to him and he brings the best out of Dawkins who cannot talk down to Lennox.


Today's word: paradigm.