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26 May 1997 Vol. 2, No. 21 THE MATH FORUM INTERNET NEWS Bogomolny's Math Puzzles | Crystals | Pi and Circle Area INTERACTIVE MATHEMATICS MISCELLANY AND PUZZLES Alexander Bogomolny http://www.cut-the-knot.com/ 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 sites. http://mathforum.org/alejandre/workshops/toc.crystal.html For examples, pictures, and crystal nets to fold, don't miss the chart at: http://mathforum.org/alejandre/workshops/chart.html Best of luck with your seminar! -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- ASK DR. MATH: PI AND CIRCLE AREA http://mathforum.org/dr.math/problems/textor5.11.97.html 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: http://mathforum.org/dr.math/faq/faq.pi.html \|/ UPDATE YOUR BOOKMARKS Cynthia Lanius' Cartography and Fractals units are moving from http://cml.rice.edu/~lanius/ to http://math.rice.edu/~lanius/ -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problem of the Week http://mathforum.org/geopow/ Internet Resources http://mathforum.org/~steve/ Join the Math Forum http://mathforum.org/join.forum.html Send comments to the Math Forum Internet Newsletter editors _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \ |

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