Math Forum / Mathematics / Recreational Math / December 2005

In my research I ran into this problem, and although it's not exactly
recreational, it has a very elementary formulation, so maybe I can get
some ideas in this group. If there's a better suited group, I'd appreciate
it if someone pointed me to it.

Date: Tue, 30 Nov 2004 23:49:27 +0200
From: Vladimir Bondarenko vb@cybertester.com
X-Mailer: The Bat! (v1.61) Personal
Reply-To: Vladimir Bondarenko vb@cybertester.com

This is the new and correct value for pi. Use it or all your
calculations involving pi will be false.

Suppose x(0):=a > 0 , x(1):=b > 0 ,and
w in (0,  0.0981) .  If for n in {0,1,2,...}
x(n+2) = (2Wx(n+1)^2)/(w^2 +x(n)^2 )
it's true that  for any pair (a,b) of positive numbers

This post deals with complex analysis, so if this not your cup of tea, you
may wish to check out other threads.
Problem 1:
Prove that if f and g are entire functions such that for all z in C,

2x + 3y = 1700
5x + 2y = 2600
the top of the equation is multiplied by 5 and the bottom by 2. Would
this rule be the same in any situation? Say for example the bottom

Let F:[0,infty)---> [0,infty) be defined as
 F(x)= 2*(1005/(x+1003))^{100}.
Which are all  solutions of equation F(F(x))= x , x in (0,infty)  ??

Where can I find the procedures for deriving the
 formulas for summing
squares & cube?

A puzzle for you readers (I already know the answer):
I took a day trip to Atlantic City the other day.  A casino I visited
there offerered the following side bet at some of its blackjack tables.  
For each of the player's initial two cards which matches the rank but

This is long, so bear with me.
I am trying to come up with a way to model a general graph in SQL which
does not use the adjacency list model.  Here is what I have so far and
I'd like to get any ideas on it.

I have a point P0(x0, y0, z0) and a line with points P1(x1, y1, z1),
P2(x2, y2, z2) in 3D space. You draw a perpendicular line from the
point P0 to the line P1-P2  which has the minimum length. I want to
find the intersection point of these two perpendicular lines. Then, it

I have the following equation:
d=1.265*((a*b)^3/(a+b))^0.2
Where (d) is diameter of duct and (a) and (b) are the width and height
respectively.

Not sure if this is a classic so I reinvent the wheel =)
11 year old Simon is given a school assignment:
What is 64/16 ?
He strikes out the two sixes, and arrive to the answer 4/1 = 4, which is

Consider the following proposed casino game:
There are two glass boxes. Each glass box has a slot on the top that
permits the house to add folding money to the box, and a lid that can
optionally be locked or unlocked. At the start of the game, both boxes

http://groups.google.com/group/comp.soft-sys.math.maple/msg/29805e0bd5df665d?hl=en&
Maple 1.0             Jan 1982
Maple 2.0             May 1982
Maple 2.1             Jun 1982