OK, so you want to send a message to somebody in Pittsburgh.

Now, let's say that all 2.4 million people in the metropolitan area are listed in the phone book. And let's say every person selects three names at random from the book and calls each of those people, exchanging numbers.

The result, according to mathematician Alan Frieze, would be a complete phone-pal ring -- every person in the metro area could be contacted through this ring. It would be possible to send a message through this ring and, by one person calling the next person on their contact list and then that person calling the next person and so on, have the message reach everybody once before circling back to you.

Maybe -- no, definitely -- this is not the best way to send a message. But there's a bit of magic in those numbers, said Tom Bohman, an associate professor of mathematical sciences at Carnegie Mellon University, and that's why scientists from around the world will gather in Pittsburgh this weekend to celebrate the career -- and 60th birthday -- of Dr. Frieze.

A math professor at Carnegie Mellon, he has been a leading force in the area of discrete mathematics known as probabilistic combinatorics, which can be used to optimize business operations and improve information networking.

The above example illustrates one of Dr. Frieze's latest theorems. In this case, the magic is the number 3 -- each person in the group calling just three other people at random would be enough to create this phone circle, said Dr. Bohman, who helped organize the "Frieze Fest" this Friday and Saturday in Carnegie Mellon's University Center.

If each person called four people at random, it would be overkill. If each person called two people at random, the circle, what mathematicians call a Hamiltonian cycle, would be incomplete.

Everyone would have at least three phone buddies, even if no one else happened to select them. Some, by chance, could have 10 or 20 buddies; on average, each would have six contacts.

Hamiltonian cycles are useful for solving so-called "traveling salesman" problems -- how a salesman can minimize costs and distances while visiting a series of cities, passing through each only once per trip.

The work can be used to analyze Internet growth and activity and peer-to-peer networks. Dr. Frieze's methods also have benefited computational medical diagnostics, guiding the design of DNA chips for diagnosing diseases or monitoring treatment.

This weekend's workshop will include presentations by researchers in discrete mathematics, operations research and theoretical computer science, with presenters from such groups as Yale University, Microsoft Research, IBM, the University of California, Berkeley, and the University of Leeds. For more information, visit the Web site at www.aladdin.cs.cmu.edu/workshops/ffest/.

Science project workshops

It's not too soon for middle and high school students to be planning projects for the Pittsburgh Regional Science & Engineering Fair March 31 and April 1 at Heinz Field and two upcoming workshops can help.

"Science Project: What You Need to Know" will be from 9:30 to 11:30 a.m. Saturday at the Carnegie Museum of Art Theater, Oakland, and "Science Projects: A Practical Approach," will be from 7 to 8:30 p.m. Oct. 25 at the Carnegie Science Center, North Side.

Both are free, but reservations are required. Call 412-237-1534.

It's chemistry week, kids!

The Carnegie Science Center and the local section of the American Chemical Society will celebrate National Chemistry Week with activities, demonstrations and shows on Friday and Saturday.

William F. Carroll, the society's president, will visit from 10 a.m. to noon Saturday, as part of his 15-city, 10-day "Extreme National Chemistry Week Tour." He will visit with students to emphasize the importance of chemistry in modern life.