Page 48 - Studio International - December 1970

Ruth Vollmer: The 'Spherical Tetrahedron' is a regular
tetrahedron, constructed from equilateral
mathematical spherical cutouts instead of flat-plane triangles.
I consider the small spun bronze piece to
suggest a five feet or taller spun-aluminum
forms one, to stand outdoors and be rocked by the

wind.
A concept of the mathematician Bernhard
Sol LeWitt
Riemann, the `Pseudosphere' is a 'false'
sphere, a surface of negative curvature.
As seen in the drawing, this curve is con-
structed on many equal circles, centred on
equidistant points on a longitudinal axis.
Beginning at the intersection of the central
circle with a perpendicular to the axis, lines
are drawn from one circle to the next con-
tinuing to the successive point on the axis,
ad infinitum. The rotation of the resultant
curve, the tractrix, around the axis creates the
Pseudosphere'
Since the lines which are the tangents of the
tractrix are all of equal length, they relate to
the curve of the `Pseudospheres' as the radii
relate to the circle of the sphere.

These pieces are not sculpture; they are ideas
made into solid forms.
The ideas are illustrations of geometric for-
mulae; they are found ideas, not invented,
and not changed.
The pieces are not about mathematics; they
are about art. Geometry is used as a beginning
just as a nineteenth-century artist might have
used the landscape.
The geometry is only a mental fact.
There is a simple and single idea for each
form; there is a single and basic material of
which the piece is constructed.
The material used has physical properties
that are evident, and useful to the form.
The pieces have a size small enough to miti-
gate any expressiveness. They are not gross
and pompous. They are of the necessary size,
neither large nor small; the form is in har-
mony with the idea.
The scale is perfect.
They are works of quality and excellence.
Hilbert*, Chapter 32, 'Eleven Properties of
the Sphere' :
`A sphere can be rolled arbitrarily between
two parallel tangent planes. It would seem
plausible that the sphere is uniquely defined
by this property. In actual fact however,
there are numerous other convex surfaces....
whose width is also constant and which there-
fore can also be rotated between two parallel
fixed plates to which they remain tangent
throughout....'
Hilbert says in the preface to his book
Geometry and the Imagination that it 'should
contribute to a more just appreciation of
mathematics by a wider range of people than
just the specialists... by offering, instead of
formulas, figures that may be looked at...
supplemented by models ... to bring about a
greater enjoyment of mathematics.'