What exactly is the square root of emotion on stage? Does anyone know how to find it?

This week’s opening of the Island Theatre production of David Auburn’s Pulitzer Prize winning play “Proof” at the Whidbey Island Center for the Arts, creates a dramatic equation so enticingly complex it may contain the answer.

The story circles around Catherine, who has spent years caring for her father, a brilliant but unstable mathematician. On the eve of her 25th birthday, a family crisis makes her face a flash of emotions. Adding baggage is the arrival of her estranged sister, Claire, and the attentions of Hal, one of her father’s former students. He comes with overachieving hopes, unmet personal goals and unclear motivation in his research.

The discovery of an ingenious mathematical proof soon takes the characters through twists of passion, humor, family betrayal and the question of inherited intelligence. A father’s den, packed with 103 notebooks, hides the clues.

“The relationships in this piece are very complex and they unfold themselves like the mystery of the proof itself,” said the show’s director, Shelley Hartle, while in the midst of running her cast through rehearsals last week.

“Proof” comes to Whidbey because of its affect on the director. Hartle saw a production of the play while in Wisconsin last year.

“I loved it, so I got a copy of the script and took it to Island Theatre and said ‘You’ve got to do this’,” she said.

The only problem was there was no one to direct the play. Hartle and her enthusiasm were soon recruited for the role.

The four actors in the “Proof” ensemble cast include some of the most well known in South Whidbey theater productions, as well as some fresh faces. Leading the cast is Deana Duncan, who last appeared on the WICA stage as Mollie in last season’s “Mouse Trap,” is Catherine.

In the program, Duncan dedicates the production to her father, Don Duncan, “Because our relationship informs almost every minute of this production for me,” she said.

To better understand this parental dedication, look to the links between Duncan, her character, and the play’s storyline.

Since reading Sylvia Plath’s “Bell Jar” in college, Duncan has had a fascination with the human ability to deal with emotional turmoil. She carries that through to the portrayal of her character.

“At the point we meet her, I don’t think we’re seeing the normal Catherine. There’s just been a family crisis and she’s in a complete depression. Her foundation is gone and she’s doing everything he can just to make it through day-to-day,” she said.

Duncan describes her father as a “real life math geek” who was offered a scholarship to Northwestern for his math skills, but turned it down.

“When I went to college I told him I was going to major in drama, and he gave me practically the same speech Catherine’s father gave her about not wasting her intelligence,” she said.

Ken Church plays Robert, Catherine’s and Claire’s father.

He has made appearances in numerous island productions including “One Flew Over the Cuckoos Nest,” “The Fantasticks,” “Glengary Glen Ross,” and last year’s hit “Moon Over Buffalo.”

Kevin Patridge makes his Whidbey Island theatrical debut as Hal, the former student who comes searching for answers for unknown reasons.

“Hal’s a helper,” Patridge said. “We connect with the sense he really does care, but part of us really does want to know why he wants to find something so badly.”

Partridge has been acting professionally and in community theater for the last decade. Last year he moved to Oak Harbor from Spokane. His previous stage roles include Tony in “West Side Story,” George Bailey in “It’s a Wonderful Life,” Danny in “Grease”; as well as numerous radio and TV voice-overs.

Kira Keeney, who plays Claire, made her community theater debut in last year’s “Little Shop of Horrors.” She followed it up with her first non-musical role as Countess in “Picasso at Lapin Agile.” Her strong musical background has lead her to serve as musical director for WICA’s 2002 summer youth theater camp and is looking toward directing music for a new adaptation of “A Christmas Carol” this holiday season.

Hartle is a 20-year veteran of South Whidbey productions with First Street Theater and Island Theater as an actor, producer and director. Her island directing credits include “The Belle of Amherst,” “Talking With,” “The Fantasticks,” “Lonestar,” and “The Winter Visit.”

She considers “Proof” a full-fledged drama that keeps ahead of the audience.

“There’s no where to hide in this script,” she said. “Everything is out there, and the actors have to rely on their own knowledge of the character and their own ability to get it across the lights to the audience.”