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For the Museum of Mathematics
MathMonday

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!

TetraOrder0  TetraOrder1 LotsOfTetras   TetraOrder3

Glen Whitney

Executive Director, Museum of Mathematics


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Comments

  1. Bruce Miller says:

    I want pieces of 3 to 4 inch thick styrofoam triangles with beveled to fit into domes. IIntend spraying concrete inside and out for a fast cheap room. I want them on a concret pad. I wnat them t bevelled at the right angles . I want buildings from dog house size to utility shed size to garage size to medium bedroom size. I need a perhaps spread sheet calculator? I want them from high density and larger sheets of low density foam? Can this be done?

    1. Sam Powell says:

      Of course. Dome calculations: for geodesic domes one of many sites http://www.geo-dome.co.uk/article.asp?uname=calculation

      For materials try Thermax and aluminum tape. Thermax is a polyiso insulation with foil facing on both sides and comes in many thicknesses. You can calculate the angles for cutting with a knife or just tape the seams on both sides. For large structures, use Bucky’s idea of starting light and keep adding to the structure until it is strong enough for the purpose.

      If you have figured out how to spray concrete, you can come up with the form. Shotcrete is a little expensive. I would use expanded wire mesh and a trowel, myself.

      Or, if the structure is really large try Paolo Soleri’s (now deceased in April) method of piling up sand, decorating, pouring the concrete, then shovel out the sand.

      Or, you could use sand bags: http://www.earthbagbuilding.com/projects/smalldomes.htm

      good luck.

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