Bonnevie Sculpture

In order to ease construction of the table, it was necessary to determine the value x, as shown:

One way to determine the value of x is to note that a cube can be dissected into 6 identical square pyramids:

Consider the following square pyramid with height h, side length a, and lateral edge length e:

The lateral edge length e is given by:

e = √(h² + ½a²)

As can be seen from the prior image, h must be ½a (as shown by the vertical yellow and red dashed lines).

Substituting for h, we have:

e = √[(½a)² + ½a²] = (½√3)a

This result can, of course, be applied to both the large outer and small inner cubes. We use subscript l to denote the large cube:

e_l = (½√3)a_l

And subscript s for the smaller inner cube:

e_s = (½√3)a_s

The distance x (see initial image) is then e_l - e_s as shown:

Substituting from above, we have:

x = e_l - e_s = (½√3)a_l - (½√3)a_s = (½√3)(a_l - a_s) ≈ 0.8660 · (a_l - a_s)

Since the dimensions of the outer and inner cubes are a_l = 24″ and a_s = 6″, we have x ≈ 15.89″ ≈ 39.6 cm.

Once these eight 39.6 cm lengths where welded in place, the other lengths were determined via direct measurement.