The triangle. It means different things to different people. To most, the triangle is simply a three-sided shape. But the triangle is versatile. It is a musical instrument. It is a romantic entanglement. And it is a drafting tool for architects. Name another polygon that can do all that.

For long-suffering fans of the Knicks, though, the triangle has come to mean something much more — a source of hope after 41 years without a championship.

When Phil Jackson sat on a dais at Madison Square Garden on a chilly afternoon in March, he promised to change the culture of the franchise. A major part of that pledge involved dusting off the triangle offense, an unconventional scheme that helped him win 11 N.B.A. titles as coach of the Chicago Bulls and the Los Angeles Lakers.

Sure, intergalactic stars like Michael Jordan, Scottie Pippen, Kobe Bryant and Shaquille O’Neal played important roles in winning all those championships, but their operating platform was the triangle, and so the triangle’s mystique only grew. It looked different (no set plays) and felt different (nobody else in the league was running it) and sounded different (all those Jackson-inspired principles).