Chemistry Reference
In-Depth Information
Fig. 2 K
3,3
.
Top
: The
complete bipartite graph
on five vertices (
left
) and
one-crossing presentation
(
right
).
Center
: Structure
of Walba's compound.
Bottom
: Kuratowski's graph
K
3,3
and Walba's compound,
with the same topology
as K
3,3
(
left
) or with
a trivial geometry (
right
)
Fig. 3 The simplest link
and the simplest non-trivial
knot, 3
1
2 The Beauty of Knots
Ancient Asiatic and eastern Mediterranean art are replete with representations of
interlaced and knotted designs and objects, symbols of continuity and eternity. The
Endless Knot (Fig.
4
) is a Buddhist symbol believed to represent the cycle of life
and rebirth, although there are other interpretations. The symbol itself is a very
angular design in which the knot traces linear sections that form right angles, which
is a representation that might help a chemist design a pathway to this beautiful
object. The central section is a grid in which each line has three crossing points,
a very suggestive drawing for a coordination chemist! It is the start of a plaiting,
weaving or basketry-type crossing, which was to find imitation to an extreme level
of beauty in the Book of Kells, an eighth century work created by Celtic monks.
In the cloisters of certain abbeys from the twelfth century, one can even find signs of
humankind's desire to thread and weave immortalised in stone (Fig.
4
).
The fascination with interweaved structures shown by the Celts was undoubtedly
related with beauty and perfection, which has lasted to the present day, spreading
and changing. The remarkable sixteenth century designs created by Albrecht
Durer and Leonardo da Vinci (Fig.
5
) were engraved and printed for subsequent
use by painters, goldsmiths, weavers, damaskeeners and needle workers [
17
].
