For the Museum of Mathematics
In theory, theory and practice are the same. In practice they are not. — variously attributed (Albert Einstein, Yogi Berra, Jan L. A. van de Schnepsheut, among others)
The best-laid plans oft are improved with a dollop of rehearsal and testing, and so it was with the scheme for building the Instant Giant Tetrahedron at the recent World Science Festival Street Fair at Washington Square Park in Manhattan, NY. Trials showed two key points: the stringing process described last time is slow and can be confusing to uninitiated participants, and the horizontal joints between successive tetrahedra are not quite rigid enough to sustain the tension generated in later generations of the Sierpinski tetrahedron construction. So with the insight and advice of Cindy Lawrence (co-executive director) and Tim Nissen (chief of design) from MoMath, the following changes to the plan developed:
1) Create anchor points at each end of every tube. MoMath staff and interns took the end caps that come with mailing tubes, pierced holes in the center of each, and then fastened an eyebolt through each hole with a nut (and Loc-Tite) on the opposite side. Then they glued each cap in place.
2) Fasten the vertices together with twist-ties through all three eyebolts at the ends of the mailing tubes that meet at that vertex.
3) Stabilize the horizontal joints with collars made from 20-cm sections of mailing tube with a slit cut along the tube section lengthwise. Before fastening two tetrahedra together horizontally, a collar can be slid onto one of the tubes meeting at the joint, the two eyebolts opposite each other at the joint can be fastened together with a twist tie, and then the collar can be slid so that half of it surrounds each of the two horizontal tubes meeting at the joint. For added stability, both ends of the collar are wrapped around with a twist tie, to prevent the slit from opening wider under the structural strains of the tetrahedron.
With these changes, the construction on June 3 went off without a hitch except for the failure of a few of the glue joints holding the end caps into the tubes. A bit of on-the-spot packing tape touch-up mended these breaks, yielding the tallest tetrahedron yet built by MoMath, as pictured below. Hope to see you at our next public building event!