FATE

Three triangles created the emblem of the Fate
Goddesses: Weird Sisters (from the Saxon wyrd, meaning 'fate'). Three
of anything arranged in triads suggested a total of nine, so in some
traditions the Fate goddesses
became nine, like the Nine Morgans of the Fortunate Isles in Celtic
myth. - In Scandinavia, the sign of fate was called the valknut, Knot
of the Vala. A Vala was either a female spirit ruling the fates of
men-a Valkyrie-or her representative on earth.

The valknut is composed of three interlinked equilateral triangles. The nine lines symbolize the nine worlds of the Norse tradition, the power of three times three. Specifically, it is a symbol of Odin. As a protector, it invokes the power of eternal unity. Its name means "the knot of the fallen (or chosen) ones."

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The Borromean rings consists of three interlocking rings, with the property that if any one of them is removed, then all three separate. The name Borromean comes from the Borromeo family of Renaissance Italy, who used them as their family "crest". The shadow, a minimal projection of the rings, is the familiar 3-Venn diagram. By minimal projection of a knot or link onto the plane we simply mean a projection that has the least number of intersections.

There is another interesting
historical context in which the rings arise. The diagram was found in
picture-stones on Gotland, an island in the Baltic sea off the
southeast coast of Sweden. These are dated around the ninth century
and are thought to tell tales from the Norse myths. To the Norse
people of Scandinavia, a drawing of the Borromean rings using triangles is known as
"Odin's triangle" of the "Walknot" (or "valknut" -- the knot of the
slain). The symbol was also carved on the bedposts used in their
burials at sea.

- techno track _Triangle Theory (Gaetano Parisio Mix)_ MP3 (192k) by Ben Sims off of _10.3 Sampler_ 12" on Theory (2001)
- track _Triangular Objects_ MP3 (192k) by Tabla Beat Science off of _Tala Matrix_