March 1965 Buckminster Fuller Lecture Notes - Page 6 of 6

Bucky at the greenboard demonstrating how to multiply by “casting out nines.” Nine is equal to three 3s which is the number of sides in a triangle . . .

We need to find ways to help men reorient themselves We need to show what is going on in universe. Like Casting out nines. Casting out nines concluded our lecture with Bucky. The rest of our time with Bucky was spent experimenting with closest packing of tetrahedrons and octahedrons (using models folded from IBM cards or marbles) and designing and building a 150- foot diameter “kissing” tensegrity dome out of bamboo. The Viet Nam war was just getting started in 1965; Bucky thought domes might be a “solution.” Closest Packing How do marbles arrange themselves under different conditions? In triangles or squares? How would unit tetrahedrons arrange themselves? How about if we add some unit octahedrons? What happens when we have octahedrons and tetrahedrons in a 1 to 4 ratio? What if the container was round, square, or a triangle? Dished or flat?

Marbles tending toward closest packing on a cookie sheet