geometry:triangle [Cauldron Wiki]

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.
====== The Triangle: 3, Trinity ======


[img]https://i.imgur.com/t3pGARk.jpg[/img]

Triple goddesses (e.g., the Wiccan maid, mother, and crone; the Morrigan; the Fates of Greek myth) and gods (the Christian holy trinity; the Hindu trimurti) are scattered throughout the world’s mythologies. The number 3 seems to have a peculiar hold on the human imagination and suggests movement beyond polarity to a balanced synthesis. The equilateral (all sides of equal length) triangle can symbolize these concepts and more.

This triangle’s properties are most interesting in relation to the circle. The triangle is in many ways its opposite: Where the circle is all curves, the triangle offers the sharpest angles of any regular polygon (a symmetrical shape with all sides and angles of equal size); where the circle encompasses the maximum area for any given length radius, the triangle is the regular polygon that encloses the least area. Thus, the triangle and circle are the respective minimum and maximum, and together can symbolize the alpha and omega. 

Mathematically, the irrational number the square root of 3 keeps emerging in various calculations using an equilateral triangle’s sides. This perhaps isn’t surprising, since if you fit this triangle snugly into a circle (so that the 3 points sit on the circle’s circumference, or rim), each side of the triangle matches the long axis of a vesica piscis for that circle.

Equilateral triangles appear in esoteric symbol systems frequently. In alchemy, the classical Western elements are all represented by triangles: fire with the point up, water with the point down, barred versions of the former and latter for air and earth, respectively. Two equilateral triangles of equal size can combine together to form a hexagram, and a circumscribed hexagram is called a hexacle. A hexacle with 6 dots added at equilateral points forms the [b]Seal of Solomon[/b], and the Seal of Solomon is in turn the basis of the later symbol called the [b]Magen David[/b] or shield of David, which is used as the main symbol of Judaism.

[img]https://i.imgur.com/u2sHLip.jpg[/img]

In Eastern traditions, this merging of up and down triangles represents the melding of male (point up) and female (point down)—not unlike one interpretation of the vesica piscis. It can also suggest the meeting of the divine and the mundane, or other various counterparts.
 
In Northern European traditions, three interlocking triangles form the [b]valknut[/b], aka [b]walknot[/b], a sign of the god Odin. 

[img]https://i.imgur.com/h3VWZ7k.jpg[/img]

The 3-dimensional analogue of the triangle is the [b]tetrahedron [/b](like a pyramid, but the base has only 3 sides instead of 4).

[img]https://i.imgur.com/biSZW5l.jpg[/img]

Next--[[geometry:square|The Square: 4, Physicality]]\\ 
Back to [[geometry:start|Sacred Geometry]] intro