Re: repeating stiffs [for Barry]


Martin Ambuhl wrote:
> Reef Fish wrote:
>
> > This is HOW I did it in my head:
> >
> > 25*24*23*22/24= 25*(23*22) = 25*506 = 12500+150 = 12,650.
> >
> > You can also get the result by noting 506 is 126 x 4 + 2.
> > Since every 4 times 25 is a 100, (126 x 4)x25 = 12,600 and even
> > you can get 2 times 25 to be 50 without your xcalc, can't you? :-)
>
> I find dividing 506(00) by 4 = 12650 to be easier than either of your
> decompositions. Mileages vary, of course.


You borrowed the 506, then multiplied the 25 by (4/4) and then
have to DIVIDE 50600 by 4, and you said it's easier?

I actually multiplied 25 by 506 in my head directly to get 12,650.

The "decomposition" was only to explain to Eddie and OTHERS how
THEY can do it without any calculator.

You may not remember the thread (in 2003) from which my quote was
taken, when I was gang-flamed by the mathematical illiterates of
rec.games.bridge (you entered only in later rounds in 2004 :-)):

RF> Let M be the 3 x 3 (symmetric) matrix with elements
RF>
RF> ( 7 3 5 )
RF> M = ( 3 1 2 )
RF> ( 5 2 1 )
RF>
RF> I can do BOTH the determinant and the inverse of M in my head
RF> (without pencil, paper, or any calculator) -- with no roundoff
RF> error of any kind.

Then John D'Errico decided his mouth needed a foot in it that
posted this immediately after my post, WITHOUT answering any of
these questions in that same post. Neither did anyone else in
rec.games.bridge did. Thus ended the Flame War I. :-)

RF> 1. What are the eigenvalues (singular values) of M?

RF> 2. I assume you know the determinant of M is the product of
RF> these eigenvalues. What value do you get for the determinant
RF> computed this way (using the product of the singular values)?

RF> 3. WHY do you NEED the eigenvalues of M to find the INVERSE of
RF> M which I can do in my head?

Want to try your hand at the determinant or answer the above three
questions, Martin? :-)

This was what John D'Errico said,

"Huh!? Never try to pass yourself off as knowing something
about mathematics and then suggest that a determinant
is a good numerical check for singularity. It just makes
someone who does know something about mathematics and
numerical analysis laugh.

John D'Errico
(Numerical analyst and applied mathematician)
===========

LOL. Where's ole John these days?

Going back to your comment

> I find dividing 506(00) by 4 = 12650 to be easier than either of your

It reminded me of the problem of calculating the distance flown by
a fly going back and forth between two approaching trains travelling
at different speeds, at a given distance apart. I assume you know
the EASY answer.

When John Von Neumann was asked the same question, he gave the
correct answer which the EASY answer would have taken much longer
to get. When asked how he did it, he replied, "That the sum of
a well-known infinitel series." :-)

Anyone care to tackle Questions 1 and 3 of the unfinished thread
because no one gave an answer to those questions? :-)

-- Bob.





















The rest was to explain to Ed

.

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