Re: Quentin (update)

Nick Cramer <n_cramerSPAM@xxxxxxxxxxx> wrote:
Quentin Grady <quentin@xxxxxxxxxxxxxxx> wrote:
On 4 Oct 2008 12:05:36 GMT, Chris Malcolm <cam@xxxxxxxxxxxxxxxxx>
[ . . . ]
Agreed. It is one reason I really WORK at maths daily. Last night I
was working at finding all the integer solutions to two resistances in
parallel that combine to give 12 Ohms. I came across a method on Mad
Maths. You can find the URL on a link from my website.

All I can remember at midnight is:

1/R1 + 1/R2 = 1/12
(R1 + R2)/R1R2 = 1/12
R1R2/(R1 + R2) = 12

I could probably write a BASIC program to find all integer solutions, but I
will have forgotten by the time I wake up. ;-(

Another interesting problem:

Given a cube with 100 ohm resistors on each side, what is the resistance
across the double diagonal of the cube? Drawing a picture makes the
solution trivial, perhaps. ;-)

Here's a visualisation exercise for the imagination where drawing is
cheating :-)

It's easy to visualise a cube, isn't it? :-)

Imagine holding a cube between finger and thumb between two corners so
that the longest diagonal runs between the corner on the finger and
the corner on the thumb. Imagine holding it up vertically in front of
your eyes. Now imagine slicing through it exactly half way down that
long diagonal in a plane cut at right angles to that diagonal.

You now have two similarly shaped half-cube bits. Imagine turning one
round to look at the cut surface. What is the shape of that cut
surface?

--
Chris Malcolm, IPAB, School of Informatics,
Informatics Forum, 10 Crichton Street, Edinburgh EH8 9AB


.

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