Let me recap the best I can for some newcomers here.
Against an orange background, a triangle appears out of a speck on the horizon, and dances to a jazz waltz tune.
Narrator: "Once there was a very jazzy triangle who just loved to dance."
On some threads posted way back when this topic came up on Yesterdayland, some people thought the music being played here was Dave Brubeck's "Take Five". No, it isn't, but this music was used last year in a Volvo ad.
Narrator: "As you can see a triangle has three sides. (Each side flashes) One, two three."
Then a different score plays in rigid 4/4 time, emphasizing the rigidness of the square.
Narrator:" One day the triangle met a very SQUARE square, who also loved to dance, in his own way." The square's form of "dancing" consists of rocking back and forth.
Triangle: "Hahahahaha! Oh boy, you're square! You don't move, you're always the same all sides and corners the same length. One, two, three, four, all sides and corners square as a box. I have THREE sides, and I can make them as long or as short as I want. I can be tall and thin, or short and fat, depending on how I feel. Boy, I sure am glad I'm a triangle."
Square:"Well, it's TRUE I can't dance as well as you can, and my sides and corners are always the same, but I don't have to decide which sides to make long and which short. I like being a square."
Triangle:"Yeah, but wouldn't you want to move around as you please, and change your shape anytime you feel like it?" Like this? (then the triangle shifts around, showing off his versatility, much to the annoyance of the anal-retentive square).
Square: "When you're a square, you're a square, and that's that! Nothing personal. You like being a triangle, I like being a square. Everybody can't be the same. Well, so long. Nice talking to you".
The square's music accompanies him as he lurches off the screen.
Narrator: "The triangle watched him go."
Triangle: "Not a bad guy", he thought, "for a SQUARE!"
Narrator: "And he danced all the way home."
Then another jazz waltz plays (in 3/4 time, emphasizing the triangle's three sides), and on the last note, the triangle shrinks back to the original speck he was, and disappears.
From what I was able to gather, the animation might have been the handiwork of a company called Aniforms, which us old-timers may remember, contributed Lorelei the Chicken to the first season of the Electric Company.
Hope this helps.