Jogging victim: A teacher, “everyone loved her.”

It was a sweet run from her Roxborough apartment into the wooded trails of Fairmount Park. Mary Katherine Ladany would have been well into her workout when the bough of a leafy tulip poplar 50 feet above her cracked.

In a random, deadly intersection of time and place, Ladany, a 23-year-old math teacher, crossed under the tree at 6:30 p.m. Wednesday, just as the dead limb, heavy as a crossbeam, fell and knocked her to the ground.

A passerby called 911 and continued on, police said. When officers arrived, they found Ladany dead, her iPod still playing.

"She was one of the best teachers I ever, ever had," said Amy Green, 17, a student at Murrell Dobbins Area Vocational School in North Philadelphia who took 11th grade Algebra 2 with her last year.

"She would make up projects with M&Ms, and we didn't move on to the next subject until we understood the material," Green said.

Ladany, who had just completed her first year on staff, demonstrated a natural gift for teaching that was matched by her dedication, said principal Charles Whiting. "Despite her short tenure, she's had a great impact," he said.

Ladany (pronounced La-DANE-ee) would come to school early and stay late to tutor students who were having difficulties. From the start, she impressed her colleagues with her candor and creative teaching methods.

"She was a real doll-baby," said Rhonda Baker, head of Dobbins' math team. "Everyone loved her. She was soft-spoken but still firm. And she believed in the kids."

A 2008 graduate of Bucknell University, where she majored in math and minored in education, Ladany was remembered as a young woman skilled at balancing all aspects of her life. As serious about athletics as she was about her studies, she also knew how to enjoy her friends.

"She was always so outgoing," said Angela Colabelli, a former classmate at Mount Saint Dominic, a Catholic girls high school in Caldwell, N.J. "I just can't believe this happened to her."

The only child of John and Patty Ladany, she grew up in Montclair. In 2004, she ranked fourth in her graduating class of 66, ran track, qualified as a National Merit Scholar, and developed exquisitely perfect penmanship.

Ladany was a fan of dollar stores and always kept a bowl of peppermints and butterscotch on her desk, along with her collection of plastic apples and other I Love My Teacher kitsch.

Her love of math was contagious. For the past two years, there had been insufficient interest to offer pre-calculus. But this September, in large part because Ladany encouraged her students to give it a try, more than a dozen students signed up for the class.