Formal Science

# Triangles Everywhere

I was recently exploring the idea of the triangle – its form, function, stability, and meanings. In Freemasonry, as in many traditions, the triangle holds significant influence in symbolic meanings.

A triangle is a polygon with three sides and three vertices. There are many forms of triangles – right, equilateral, obtuse, acute, isosceles, and scalene. There are also oblique and degenerate triangles. Triangles may be multiple types. Triangles are generally believed to be two-dimensional objects whose interior angles, at least in Euclidean space, equal 180 degrees. They can be various shapes but the ones most often seen are right triangles and equilateral triangles.

Of the triangle knowledge from history, the famous philosophers Pythagoras, Plato, and Euclid are known best for theorems, ideas, and esoteric supposition surrounding the form. The form is so basic that it’s most likely older than written history. Ancient petroglyphs, such as those from Columbia, the Sierras in North America, and Mexico, show humans with bodies and heads in the form of triangles. This is a basic shape that mimicked the human form, with wide shoulders and narrow waist, or a wide head crown and narrow chin. There isn’t anything to indicate, in-depth, the symbolic meaning of the triangle other than it being incorporated into the human form.

The Egyptians used the triangle quite often, generally in the realignment of land plots after the Nile floods but also in architecture. In a 2000 thesis article regarding the “sacred triangle,” the author asserts that Egyptians knew and used, even in the Old Kingdom, the “sacred triangle” of 3:4:5. Indeed, the author goes on to state that using straight vertices, or a “simple, straight vertical pole,” to find location or identify specific time of day or days of the year. While this is a heavy-mathematics article, the reader might find some deeper, symbolic meanings in the geometry.

During the 6th C. B.C.E., the School of Pythagoras became known for its theorem regarding the formation of the ‘sacred triangle.’ Pythagoras left no mathematical writings of his own, while Euclid and Plato did. Thales of Miletus is really the creator of basic mathematics and geometry, and probably the first to give us theorems about the triangle. Pythagoras, who created the words philosophy and mathematics, is more well-known and did much to bring the form of the triangle into deeper meaning.

To Pythagoras, the number 10 was the holiest of numbers; the tetractys is a triangle form of 10 dots, created by interlinking the dots into nine triangles forming the 10th, larger triangle. It is used to symbolize the creative forces of the universe. From ancient-symbol.com, “In the figure, the first row has a single point that is representative of the Creator, the active principle, the divine power behind all creation and is associated with wisdom. The second row contains two points that represent the passive principle and are associated with friction, movement, impulse, strength, and courage. The third row with three points signifies the world coming out of the union of the above two, a union of physical and mental balance and is associated with harmony. The fourth row has four points that represent the four liberal arts & sciences that complete the world. These four points symbolize the four elements of earth, fire, air, and water.” This was, generally speaking, the first time that the philosophical meaning of a number, its holiness and perfection, being derived from pure mathematical reasoning rather than from inductive reasoning. It was more than the total of our fingers on our hands. Another interesting article on the triangle and tetractys, among other things, can be found here: http://www.projectawe.org/blog/2015/12/21/up-and-down-the-monochord-part-iii-triangle-trinity-unity. The author of this blog does a very good and thorough job of digging into these ideas, and I would highly encourage everyone interested in these subjects to read it.

In the alchemical writings of the Middle Ages, the classical elements of hermeticism were based off the form of the triangle, turned upward or down, with a line to denote the opposite or without to indicate the base elements. The conjoining of fire and water is indicative of balance and achieving perfection. The triangle is also seen in the “triangle of art” also known as Solomon’s Triangle. The circle in that triangle represents the space where spirits are called, with the triangle representative of the safe space from which the magician worked.

Triangles in astrology are seen as very positive, and a grand trine, or golden triangle, is seen as a creative, harmonious flow of energy in a person’s life; they generally are composed of the objects being in the same elements, in the form of an equilateral triangle.

Triangles are a form of stability, where two extremes are balanced by a third point. Triangles are everywhere in Freemasonry, overt and subtle, and have different stories surrounding each. These different stories speak to individuals differently even if the core remains the same; depending on the degree being worked and studied, the aspirant may find different aspects of the same truth. These truths are not much different than the ancient Egyptians and Greeks found and used in their daily lives. There are always extremes and balance is achieved by that third, divine point. One might also see that all emanates from the Divine, the single point, which may also turn into that point within a circle which is perfect balance. The perfect man may be the one who finds equilibrium during whatever storm shakes him. Taking this symbolism into our daily lives and applying it to our relationships with people is really the value of the study of symbol. We can work toward being the middle point between extremes, able to see both sides in equal measure. A more holistic view of those things that permeate our lives creates a better person.