Please forward this error screen to 193. Borromean links, cannot be exactly circular. Apart from indicating which strand crosses over the other, link diagrams use the same notation to show two strands crossing, as graph diagrams use to show four edges meeting at a common vertex. In knot theory, the Borromean rings are a simple example of a Brunnian link: csc chennai contact each pair of rings is unlinked, the whole link cannot be unlinked.

There are a number of ways of seeing this. Another way is that the cohomology of the complement supports a non-trivial Massey product, which is not the case for the unlink. In arithmetic topology, there is an analogy between knots and prime numbers in which one considers links between primes. Therefore, these primes have been called a “proper Borromean triple modulo 2” or “mod 2 Borromean primes”. The Borromean rings are a hyperbolic link: the complement of the Borromean rings in the 3-sphere admits a complete hyperbolic metric of finite volume. The standard 3-strand braid corresponds to the Borromean rings.

In the standard link diagram, the Borromean rings are ordered non-transitively, in a cyclic order. Similarly, in the standard braid, each strand is above one of the others and below the other. The Borromean rings as a symbol of the Christian Trinity, from a 13th-century manuscript. The name “Borromean rings” comes from their use in the coat of arms of the aristocratic Borromeo family in Northern Italy. Norse image stones dating back to the 7th century. The Borromean rings have been used in different contexts to indicate strength in unity, e.

In particular, some have used the design to symbolize the Trinity. The rings were used as the logo of Ballantine beer, and are still used by the Ballantine brand beer, now distributed by the current brand owner, the Pabst Brewing Company. The Borromean rings, especially their mathematical properties, were featured by Martin Gardner in his September 1961 “Mathematical Games column” in Scientific American. In 2006, the International Mathematical Union decided at the 25th International Congress of Mathematicians in Madrid, Spain to use a new logo based on the Borromean rings. A stone pillar at Marundeeswarar Temple in Thiruvanmiyur, Chennai, Tamil Nadu, India, has such a figure dating to before 6th century. Similarly, a monkey’s fist knot is essentially a 3-dimensional representation of the Borromean rings, albeit with three layers, in most cases. Using the pattern in the incomplete Borromean rings, one can balance three knives on three supports, such as three bottles or glasses, providing a support in the middle for a fourth bottle or glass.

Discordianism, based on a depiction in the Principia Discordia. Crystal structure of molecular Borromean rings reported by Stoddart et al. Molecular Borromean rings are the molecular counterparts of Borromean rings, which are mechanically-interlocked molecular architectures. Named after the coat of arms of the Borromeo family in 15th-century Lombardy. The Geometry and Topology of Three-Manifolds, p.