## Dear Alexandria Jones,

We continue to excavate the ancient building complex, which I believe may have been Pythagoras’s school. Yesterday, one of our digging crews uncovered a mosaic tile floor in the courtyard. The pattern of the tiles alternates between two square designs. (See enclosed sketches.)

During your family’s recent visit, you expressed an interest in the mathematical ideas of Pythagoras. Could you or your father offer us any insight into what these tile designs may represent?

I look forward to your response.

Sincerely,

Sofia Theano, Ph.D.

Crotone, Italy

## Puzzling Out the Pattern

Ales showed the letter to her father. “I’m confused, Dad,” she said. “I thought you called Dr. Theano, *Sonya*.”

“Well, yes,” Dr. Jones replied. “That was her nickname. But now that she is a professor herself, it appears that she has gone back to using her given name.”

Alex nodded. “That makes sense, I guess. What do you think of these tile patterns?”

“That is an interesting puzzle,” he said. “Perhaps it would help if you got out a large sheet of paper and traced the designs together, as they would appear on the courtyard floor.”

## The Mosaic Tiles

Leon walked in as Alex was drawing and leaned over her shoulder. “Hey, look,” he said. “All the triangles are the same size. See how they fit next to each other?”

“Hmm,” murmured Alex. “And it looks like the small leg of the triangle matches the small square, and the longer leg matches the medium square.”

“And the big, tilted square goes with the hippopotamus.”

Alex laughed. “You mean, hypotenuse. I think we might be on to something. But how can we tell for sure?”

## To Be Continued…

Read all the posts from the May/June 1999 issue of my ** Mathematical Adventures of Alexandria Jones** newsletter.

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