Re: Plausibility Check


Brian M. Scott wrote:

No, it isn't.

Of course it is the begin of a proof, the begin of my proof
I gave to a poster via e-mail a couple of years ago. You
can begin a number column for the approximation of the
square root of 2 with any pair of numbers, for example
1 and 1, or 1 and 3:

1 1 2
2 3 4
5 7 10
12 17 24 and so on

1 3 2
4 5 8
9 13 18
22 31 44 and so on

Consider the first, third, fifth, seventh, nineth ... line,
square the middle number of each line, and subtract
the product of the first and last number. It will be -1
in the case of the first number column, 7 in the case
of the second number column:

1 x 1 minus 1 x 2 equals minus 1

7 x 7 minus 5 x 10 equals minus 1 and so on

3 x 3 minus 1 x 2 equals 7

13 x 13 minus 9 x 18 equals 7 and so on

Now let us formulate the algorithm algebraically:

a b 2a
a+b b+2a 2a+2b
3a+2b 4a+3b 6a+4b

Consider the first and the third line. The square of
the middle number minus the product of the first
and last number of line 1 equals the square of the
middle number minus the product of the first and
third number of line 3, hence:

bb - 2aa = 16aa + 24ab + 9bb - 18aa - 24ab - 8bb

bb - 2aa = bb - 2aa

This proves that the mistake remains the same,
while the numbers increase.

qed Franz Gnaedinger

.

Relevant Pages

  • Re: relation between twin primes and Sophie Germain primes
    ... Whoever seem the fatal segment and offset it minus its square. ... business was injured, joint, and corresponds between the autumn. ...
    (sci.crypt)
  • Re: Your Own Useful Skills
    ... remember (YMMV of course) than "minus b plus or minus the square root ...
    (rec.arts.sf.written)
  • Re: TOT: Separated Extra Low Voltage user configuration issues
    ... In the seventies you wouldn't have needed to ask that question. ... If AX squared plus BX plus C equals nought then X equals minus B plus or minus the square root of B squared minus four AC all over 2A ...
    (uk.tech.digital-tv)
  • Re: box headings
    ... Leo Kerner wrote: ... > square, or button, with a plus sign in it followed by the words ... > minus and a new line appears for the particular item, ... Brian Tillman ...
    (microsoft.public.outlook)
  • FS: NOS Williams spares
    ... All are NOS ... Stand up targets, ... Yellow square rectangle ... Revenge From Mars poster ...
    (rec.games.pinball)