Cat Bordhi, who found joyful rebellion in thinking up new techniques for knitting socks, cowls and other clothing, and whose books encouraged others to question the orthodoxy of that age-old practice, died on Sept. 19 at her home in Friday Harbor, Wash. She was 69.

Her daughter, Jenny Low, said the cause was cancer.

Ms. Bordhi (pronounced BOARD-ee), who learned to knit from her grandmother, had a revelation one day in 2000 when she picked up her needles to make a pair of socks and was confounded by the complicated methods instruction manuals dictated. There had to be an easier way, she thought. She came up with a simplified technique using circular needles — two needles connected at the bottom by a cord. Her process started at the heel, rather than conventionally, at the toe or the cuff.

She decided to share the news of her discovery, and in 2001 she self-published a book called “Socks Soar on Two Circular Needles.”

“If you love learning new skills, delight in knitting architecture, love to knit socks or just have cold feet,” she wrote, “I welcome you to the world that lies within these pages.”

In its first decade, Ms. Low said, “Socks Soar” sold more than 100,000 copies.

She published five more printed knitting books, with titles for both devotees (“New Pathways for Sock Knitters,” 2007) and the merely knit-curious (“Personal Footprints for Insouciant Sock Knitters,” 2009), in addition to five e-books and numerous patterns.

In the patterns she provided in books and online, as well as in tutorials she gave on YouTube, Ms. Bordhi blended creativity in linguistics and fiber arts. In 2013, she published a book dedicated to woolen slippers and bootees called “The Art of Felfs,” a word she used to describe “felted elfin footwear.”

Ms. Bordhi’s best-known knitting design is for a moebius cowl, a contiguous neck wrap that twists. Before 2005, manuals taught knitters to construct moebiuses by making a scarf, twisting it and then sewing together the ends. But Ms. Bordhi woke one night with an idea for a different method: a circular needle moebius “cast on” — a term used for the process of getting the initial loops of yarn onto needles — that would allow the moebius to be made in a circle without end.

Ms. Bordhi published this method, free of charge, on her website, along with a YouTube video that has been viewed more than a million times.

“The moebius has no beginning, no end, no top, no bottom, no inside, no outside,” said Jan Hamby, an owner of Fair Winds Farm, a sheep farm in Quarryville, Pa., where wool is harvested. “It is an infinite thread and the very essence of who Cat was.” Ms. Hamby first met Ms. Bordhi when attending a workshop she led on forensic knitting, in which students deepen their understanding of knitting by deconstructing pieces.

Ms. Bordhi spent much of the last two decades hosting fiber-arts retreats in Friday Harbor, which quickly sold out. She also organized group knitting excursions to Peru, Mexico, Scotland and Iceland that were so popular, participants would sometimes book three years in advance.

“We would walk around small villages and happen upon a plaza where we would stop to knit,” Jim Petkiewicz, who organized the excursions with Ms. Bordhi, said in an interview.

Locals occasionally gathered and joined in “I learned from Cat,” Mr. Petkiewicz said, “what a tool knitting could be for breaking down barriers.”

In February, Ms. Bordhi hosted a knitting retreat in Friday Harbor. She called it “Let the River Carry You,” a reference to one of her designs, for a cable-knit cowl. She encouraged students there to let their creative instincts flow.

“The basis of that pattern, she would tell her students, is to imagine yourself as a river,” Mr. Petkiewicz said. “A river doesn’t ask for permission; it goes up and over, it goes underneath.”

Kathryn Anne Elizabeth Gardiner was born on March 2, 1951, in San Francisco. Her mother, Jackie Gardiner, a nurse, died of breast cancer on Kathryn’s sixth birthday. Three days later, her father, Dr. Wally Gardiner, a physician, committed suicide. Kathryn and her siblings Tom and Diana were adopted by family friends, Dr. Glen Haydon, a physician, and Helen (Goodwin) Haydon, a homemaker.

After graduating from the University of Santa Barbara with a degree in Russian literature and language, she worked as a seamstress and moved between Menlo Park, Calif., and the San Juan Islands in Washington, before settling in Woodside, Calif., where she married Louis Bordi in 1981. Their daughter, Jenny, was born in 1983, and they divorced in 1985. (Ms. Bordhi changed the spelling of her name to Catherine and then settled on “Cat.” She also added an “h” to Bordi to assert her own identity as she became more focused on her publishing career.)

To support her family, Ms. Bordhi made teddy bears with movable joints. She sold 5,500 “Chocolate Bears” for about $200 apiece, her daughter said, before she developed back pain from hunching over a sewing machine.

Ms. Bordhi and her daughter moved to Washington State, eventually settling in Friday Harbor, on San Juan Island. She married Michael Schifsky in 1988; they divorced after three years.

She started working as a public-school teacher in 1992 and passed her knitting skills down to her students at Friday Harbor Middle School because, she said, they could better focus on their lessons when busying their hands with the methodical and meditative process of knitting.

In 2003, she took a step away from craft writing and published “Treasure Forest,” an adventure book for young readers that was meant to be the first in a trilogy. In 2004, the book won a Nautilus Award for young-adult fiction.

In addition to her daughter, Ms. Low, Ms. Bordhi is survived by a grandson; two brothers, Tom and James Haydon; and two sisters, Diana Rabbe and Martha Haydon Grigs. Another brother, Fred Haydon, died before her.

Ms. Bordhi had breast cancer twice and endometrial cancer once.

“She was really unique in how she approached cancer,” Ms. Low said. “She chose to view the cancer in her body as a friend she was on a journey with.”

This summer, almost a year after learning she had cancer yet again, Ms. Bordhi posted on her blog about her impending death and shared a pattern for her Rio Catalina Cowl. The winding cable design, she wrote, “teaches you to let go.”