Math Forum / Mathematics / Recreational Math / May 2006

A simple geometry problem can be reduced to a solution of the following system of equations:
1) a^2+x^2 = b^2+y^2 ,
2) a*b-x*y = b*x+a*y .
Find x and y.

Let S be the set of squarefree integers >=1. Evaluate
sum_{x in S} x^(-2)
Hint: It's not frightfully deep.

On the NY Times web site, there is a story and picture about a hollow
molecule composed of 16 atoms of gold.  It looks like the figure is an
irregular polyhedron where some vertices have six triangles meeting and
others have four.  The article is "16 Golden Atoms in Search of a ...

Can somebody explain to me how I may do the following calculation
using a spreadsheet?
I have . . .
Total Profit (not total return)

A cylindrical pot has the diameter d = 16 cm and the height h = 8 cm. The bottom edge of the pot is rounded with the radius r = 1 cm. Determine the volume of the pot.
Best regards,
   Avni

Determine the cube with the maximum length side which fits in the regular tetrahedron with the unit length side.
Best regards,
   Avni

A circle of 10 cm. diameter has a smaller one drawn inside of it and touching the circumference of the larger one. A chord in the larger circle is tangent to the smaller circle. If the sector area so formed is equal to the area of the small circle, find its diameter.

A body traveling 16.5 m/s is decelerated to zero over 275 m. What was
the duration in time? The body (a train, of course) has mass of 3.1e6
(3.1 million) kg.
Standard equations -- I think:

Any text can be compressed by using a table of abbreviations.
For example, a frequently occurring phrase such as "of the"
could be represented by some shorter character-string.
Then a full text could be compressed into a table of abbreviations

A spiral consists of infinitely many linear segments parallel to the sides of the equilateral triangle with unit length side. The first segment of the spiral is the side AB of the equilateral triangle, and the ratio of any two consecutive segments is 5/4. Determine the distance ...

In an article in the May 2006 Harper's magazine, Michael Hudson says in an article titled "The New Road to Serfdom: an illustrated guide to the coming real estate collapse" (page 43):
    The eighteenth-century philospher Richard Price identified this miracle
    of compound ...

There are three squares on the left of the page and their are
squares on the right, right across from each other.  You need to mak
a line from each square on one side to each square on the other side
BUT the lines CANNOT touch.....  If someone could help me I woul

I'm a consumer of mathematics, not a mathematician.  I can't solve for x, but
would very much appreciate it if someone else could.  :-)
y=(1.1/x)/SQRT(((1.27*0.000555*z*1.1/x)^2)-(0.5*(1.27*0.000555*z*1.1/x))+1)
THANKS!

2 cubic boxes having totally reflective surfaces on the exterior are in
circular orbit around the sun. 1 face of each box is permanantly facing
the sun. this face has a 1 mm diameter circular hole. the interior of
one box is painted white, the other is black. what is the equilibrium

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Some Maple customers are worried with noise caused by Maple
during computations.
For example, renowned Prof Dr Edwin Clark