I know D'Antoni has his Seven Seconds or Less offense, but with the additions of Carmelo Anthony and Tyson Chandler, and the subtraction of Steve Nash, I really see the Knicks as perfect candidates for the Triangle Offense. Maybe I'm totally off base, but here's a few reasons why:
Melo as the playmaker: Melo is probably the team's best passer right now, so why force Toney Douglas and Mike Bibby to do a job he could do better? The triangle allows your wings to do more playmaking, and is similar to SSOL in that players react to their environment. Here's an impeccably-timed play the Knicks ran only a handful of times last year: Melo gets in triple-threat position at the top of the key. Amare is on the other side along the baseline. This is where the defense THINKS they know what's going to happen - Melo's gonna chuck something. But then Williams or Landry streak along the baseline to the opposite side, anticipating a corner poop, while Amare curls up to the top of the key opposite Melo. As soon as one of the interior defenders turns his head to react to the corner streaker, BAM, Amare curls off to the basket. and Melo just drops it into his hands. KER-DUNK.
There is no clear-cut distributing PG. Duh. This is similar to the last one. Why shoe-horn Toney Douglas into being Steve Nash, when he's obviously a more bad-ass Ron Harper? He's the team's best outside shooter, but - this will be a recurring theme for the team's guards - he struggles to create his own shot. The Triangle will allow him to play off the ball. The learning curve to turn him into this kind of perimeter player isn't nearly as steep as it is to turn him into a pick and roll genius. With the Knicks likely to play a combo of Toney/Bibby/Shumpert at the two guard slots a good portion of the season along with Melo, this gives the Knicks the ideal three playmakers to run the offense.
The Melo/Amare Pick and Roll: Again, this was run only a handful of times last season, but it seemingly never failed. My original hypothesis was that D'Antoni didn't want to mess with what his guys knew, but then I saw footage of a Melo/Nene pick and roll that they ran over and over to much success. And we all know Amare isn't shy about that play. I hope they're working on this play RIGHT NOW.
Amare's Range: There's a whole chunk of STAT's game that the Knicks don't even use. His outside shot is just as good as his mid-range. The triangle will allow him to force big men to trail him out to the 3-point line. This not only gives the Knicks another outside shooter, but also opens up more opportunities for Chandler.
The Revival of Landry: After the Melo trade, the Knicks leaned on Fields to be a creator for himself with the ball in his hands, but that's expecting a bit much of him. The Triangle offense is a boon to opportunistic players who can read the situation and make plays happen out of nowhere. And with Turiaf gone (it's ok to shed a tear), the Knicks' most opportunistic player is now Landry Fields. With Melo as a playmaker and Amare down low, opposing defenses will not be paying attention to a young Robert Horry Landry Fields, and that is when he'll make them pay. Everything I just said about Landry applies just as much to a healthier Andrew Bynum Tyson Chandler, only on the inside (also, see how I just made Chandler's health risk look like a good thing?).
Shumpert: We haven't seen a minute of this guy in the NBA yet, but I bet he looks better playing from the post than he does from the perimeter.
Sorry for the bullet-list. I really think you all can handle paragraph form, but I'm just lazy. Feel free to let me have it in the comments.