Math Forum / Mathematics / Recreational Math / August 2005

Having on formal graph theory or topolgy training I hope this question
isn't too trivial. Actually, I hope the ANSWER is trivial!
Suppose I'm a bug living in a universe which consists of a graph of
nodes connected by edges. I can move from node to node, but the

What the Kansas Board of Education has done
is unconstitutional because, either explicitly or
implicitly, the only alternative to evolution as the
explanation for how life arose is "magic" (or "God").

Does the central axis of a cone pass through the central point of an elipse which is a conic section taken at 90 degrees to one part of the cone's surface (not the base)?
Many thanks
Jonathan

For anyone interested in BASIC and embedded Intel Assembler programming
and things mathematical, I've just updated my website "Mister T's
Mathematical Diversions" with;
*Spyglass - enables you to magnify a circular region in a picture, just

For k = 2
 (f(x))^k = f(kx) + k
is solvable by inspection:
 f(x) = 2 cos(cx).

I read that, other than 1, 144 was the only square Fibonacci number.  I'm
wondering how this is proved.
Best wishes, Jim

In the following
SUM{Y_k}:=Y_0+Y_1+...+Y_n and C(n,k):=n!/(k!(n-k)!) .
Suppose that  f(x)=SUM{A_k*X^{n-k}} has only real roots.
If p,q,r,s,t are non-negative  integers (q >=1 , n >= 2 ) and

In the classic demonstration of the impossibility of trisecting an angle by a compass and straight edge, the example is given of a 60 degree angle which is subjected to an analysis that relies on trig formulas.  A successful solution would require the factoring of a cubic ...

I'm looking for documents out on the internet on algorithms for
efficiently packing squares in squares (2D & not bin packing). I've
found some good stuff, but if anyone knows any good sites or info, I'd
really appreciate pointers.

A friend of mine has just released a new board game and he has asked me
to help work out a few of the dice probabilities involved in the game
for a page on his website. I now wish I'd paid more attention at school
as I'm having a few problems getting my head around a few of the

How can it be proofed, that the largest number of self intersections of n
lines A1A2, A2A3, A3A4....AnA1, there n is an even number and > 3 and there
are no three lines intersecting at the same point, is n*(n-4)/2 - 1 ?

Does anybody know a simple mathematical definition of zig-zag lines? I
googled, but I did not find what I was looking for.
Cheers,
Nils

The title says about everything : winding a rope around a cirle with a
pencil attached to it, and then drawing a curve, starting at angle zero on
the circumference while un-winding the rope.
Like this, we get two angles to consider at any point we stop : the angle

I didn't find this puzzle in the archive, so maybe it's new for you:
A cube (edges of length 1) stands in front of a vertical wall on horizontal ground. To which height (h) does a ladder of length l reach, which stands on the ground - and obviously touches both cube and wall?
This ...

This is my third question this week, and it is still on the same topic!  If
you want, I'll go away! :-)
Consider the following:
We start with a parameterized surface, that is P(u,v) = (X(u,v), Y(u,v),