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Volume 2, Number 21

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  26 May 1997                                 Vol. 2, No. 21


   Bogomolny's Math Puzzles | Crystals | Pi and Circle Area

                  Alexander Bogomolny


An award-winning Math site with games, puzzles, quotes,
and short essays on a variety of topics. Sections on
arithmetic, geometry, algebra, and probability offer a
rich lode of explanations and information. Features:

- The CTK Exchange, a Web discussion area for questions
  and answers about math problems
- Java-enhanced probability problems, including the Monty
  Hall dilemma and Bertrand's Paradox
- "Things Impossible" - trisecting an angle, doubling a cube,
  squaring a circle...
- The Eye Opener Series, where Java visualizations help
  solve problems and construct proofs
- The Inventor's Paradox, on the investigative part of
  doing mathematics
- "Do you know that...," math facts and curiosities
- Fast arithmetic tips and their purpose
- Essays on such topics as "Mathematics as a language,"
  "Proofs in Mathematics," and "The many ways to construct
  a triangle"

Bogomolny also offers a glossary of math words and a 
bookstore for ordering math books on the Web.


                   POLYHEDRA: CRYSTALS
                    Suzanne Alejandre

From the emailbag:

   I am doing a seminar on crystals. I was wondering
   if you could guide me to information on the Web 
   that is not very advanced and is related to 
   mathematics/physics. Thank you so much.
                                         - Ruxandra

Hi Ruxandra,

Suzanne Alejandre's Web unit on polyhedra makes connections
to the physics and chemistry of crystals and presents
information at a variety of levels with links to many other

For examples, pictures, and crystal nets to fold, don't miss
the chart at:

Best of luck with your seminar!



   If pi truly goes on and on forever without repeating, 
   is it impossible to find the EXACT area of a circle?
                                         - Jason Textor

Sort of. If you know the exact radius of a circle and you
use the formula Area = Pi*Radius^2, you have found the
exact answer. So for instance, if the radius of a circle
is 3, then the area of that circle is _exactly_ 9 Pi. The
decimal representation of this answer can be calculated to
whatever accuracy you need by calculating Pi.

Here's another thing to think about. Let's say the radius
of the circle in question is exactly "2 over the square
root of Pi" feet, which is *about* 13 and a half inches.
In this case, it is impossible to find the exact decimal
representation of the the radius, but the area is exactly 4.

Fortunately, in the real world you rarely really need more
than eight or nine decimal places, even in "crucially exact"
sciences like space travel. Besides, if you knew Pi to a
'gazillion' places and could find the area to a 'gazillion'
places, where could you write down the answer? Or where
could you find a person with the patience, or life-span, to
listen to the answer?
                                         - Doctor Math

For other interesting questions and answers about Pi, see
the Dr. Math FAQ:


                    UPDATE YOUR BOOKMARKS

Cynthia Lanius' Cartography and Fractals units are moving from to


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