10 Apr

Archimedean Variations

So I had zeroed in on the proof of the Archimedean volume relationship as the source of my giveaway for G4G13. But how to create an interesting variation? The first thing to notice is that the function of h that appears in the proof in the cross-sectional area of of the cone, namely h², could […]

09 Apr

Mathematical Free Association

So it became time to decide on Studio Infinity’s giveaway at the 13th Gathering for Gardner (G4G13). By tradition, at least, it’s considered a plus for giveaways to connect with the number of the conference — 13 in this case. So this mathematical free association starts with the number 13. What thoughts does 13 evoke? […]

05 Apr

GGSF: Calculations

This post just takes care of some of the calculations used in planning the Golden Gate STEM Fair event. First, the plan was to make the structure shown at the right: a regular tetrahedron on top of a regular octahedron. Moreover, the resulting construction was intended to be five meters tall. Hence, the question arises: […]

05 Apr

An Oct-Tet of Cubes

In the last MathStream post, we concluded that if you took spheres with holes at the points indicated by black dots in the diagram below, you could connect them with struts to form a lattice composed of alternating octahedra and tetrahedra. But for building large-scale constructions, we’d like something comprised of components that are a […]

04 Apr

More Spherical Construction

The ease with which we could draw an equilateral triangle on the sphere naturally leads to wondering whether other constructions work out so nicely. For example, can we construct the square of points that would be needed to locate the holes for building a regular octahedron from styrofoam balls and sticks? Since the central angle […]

04 Apr

Ruler and Compass on a Sphere

For this project, I needed to figure out (a) where should the holes be in spheres to connect them by straight lines to form a regular tetrahedron, and (b) how to locate those points on a physical sphere. The diagram makes part (a) fairly straightforward. We can see that the angle between any two holes […]

07 Nov

The icloseidodecahedron

When I set the goal of creating a new tensegrity structure for the Storm King Art Center workshop, I decided that I wanted to create a highly regular, symmetric structure, to contrast with the more free-form, organic style of Snelson’s Free Ride Home at the Center. (Snelson also created many very regular tensegrity sculptures himself.) […]

07 Nov

Balance of forces

As mentioned at the end of the last MathStream post, the actual shape that the six-strut tensegrity structure takes on is close to, but not quite precisely, a regular icosahedron. And that fact immediately makes you want to build a tensegrity structure that will under ideal circumstances assume the shape of a truly regular icosahedron. […]

07 Nov

The icloseahedron

So maybe you’ve made the classic six-strut tensegrity (or perhaps you’ve just looked at the pictures) and you’re wondering what shape that is, exactly. Naturally, since mathematics is among other things the science of shape and structure, understanding that is going to involve a little math. And in mathematics, sometimes it’s easiest to understand something […]