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When professors from the mathematics and statistics department at Northern Arizona University reach out to the community, of course they bring the math goodies with them.

With the Northern Arizona Math Circle, math is touted as fun and diverse. The sessions, held at Northland Preparatory Academy, have students working on problems that test their spatial reasoning and logic.

This week, they mulled over hexagons made of triangles. Knowing that a rhombus (or diamond) is formed by putting two triangles together, how many diamonds could they get from their assorted hexagons?

It's a geometry puzzler for math professors as much as high schoolers. Steve Wilson, the professor leading Thursday afternoon's after-school discussion, and his colleagues might have an answer, or they could just as well have a variety of answers.

As did the younger scholars.

David Ganey pulled four triangles out of his 1x2x2 hexagon. As he sketched it on the board, the thinking came aloud in real time to six triangles. Then 12. Then back to six.

"It makes sense now," he mused. "... No. No it doesn't."

He crossed out the numerals before walking away from the "6."

"He's placed his chips in the middle of the table," Wilson said in a playfully hushed tone.

"I'm all in," David quipped.

This is math for fun. The four students working on the puzzle scratched their pencils quietly over their graph paper, but also swatted each other with friendly jabs.

Mandy Xu concluded that a 1x2x3 hexagon yields eight triangles.

David wasn't sure.

"No Mandy, it's not eight," he said.


This is math for fun. Bonding, even, since academic exercise is how math circle kids roll.

On Monday, they'll pick up where they left off. They worked straight through the time allotted for the Thursday session and seemed eager to dissect the possibilities.

"These are very bright kids," Wilson said. "I'm really pleased with the progress we're making here."

The new program is funded through a Dolciani Mathematics Enrichment Grant from the Mathematical Association of America. Parents and students can e-mail to get involved.

Hillary Davis can be reached at or 556-2261.


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