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Triangle Symbolism

Trinity, ternary law and the Three Worlds
number 3, creative triangle

Geometry of triangle

First geometric shape of third dimension
triangle's formation

Constructing the triangle

The radius can be likened to a straight line defined by two points: the center and the point of contact with the circumference (figure 1).

But this second point can itself be the center of a new circle as shown in figure 2.

From then on, the center becomes the middle of a segment through which rises a perpendicular that intersects the first two circles by two points of contact (only the high point is shown in figure 3).

By connecting these three points we obtain the figure of the equilateral triangle (figure n°4).

« Among these many triangles, there is one that we regard as the most beautiful to the exclusion of the others: it is the one from which is formed the third triangle, the equilateral triangle. »

Timaeus ~ Plato
triangle derived from Vesica Piscis

By extending the two oblique sides, we obtain two other crossing points with the two initial circles. If we add the low point to the graph we obtain the 3rd triangular number, the number 6.

The triangle has the particularity (with the square and the hexagon) to completely cover the plane (2D space) without leaving any empty space. Only these three figures benefit from this property.

By reproducing this operation along the circumference one obtains 6 equilateral triangles (figure n°5) inside a circle, i.e. hexagonal paving. The center of the circle becomes the seventh point, the only one common to all six triangles.

The numbers 1 and 2, although dividers of the circle, do not form a closed figure. The equilateral triangle or trigon is therefore the first of the polygons.

« Tao begets one. 
One begets Two. 
Two begets Three.
Three begets all beings. »

Lao Tseu ~ Tao Te King

Triangular polygons

The trigon, or 3-sided polygon, is the first of the 22 polygons of the circle. It is associated with Time (which is successive), as well as the polygons of its family that it generates by simple duplication), the polygons with 6, 12 and 24 sides.

  • The triangle: the ternary time (past ~ present ~ future)
  • The hexagon: the 6 days of Creation
  • The dodecagon: the 12 months of the year
  • The 24-sided polygon: the 24 hours of the day
triangular polygons

Polygons of time

Triangular numbers

The triangular numbers are obtained by adding the counting numbers:

  • 1 + 2 = 3
  • 1 + 2 + 3 = 6
  • 1 + 2 + 3 + 4 = 10

If the triangular number three has the shape of an equilateral triangle, following the homothetic development, the other triangular numbers will also have a regular shape, and the similarity of the shape is preserved in the development.

The tetrahedral numbers are obtained by adding the triangular numbers:

  • 1 + 3 = 4
  • 1 + 3 + 6 = 10
  • 1 + 3 + 6 + 10 = 10

From triangular to tetrahedral numbers

« However, the body type always has depth, and depth is, of all necessity, enclosed by the nature of the surface, and any surface of rectilinear formation is composed of triangles. »

Timaeus ~ Plato

Symbolism of Triangle

Trinity and Ternary

Symbol of divinity

The number 3 - the first of the odd numbers (one being considered the number principle) - is symbolically represented by the divine figure or triangle.

Egyptian symbol of divinity, Pythagorean symbol of wisdom, Christian symbol of the Trinity, the equilateral triangle, the first closed figure of the second dimension (2D), represents the archetypal form of geometry.

The holy trinity and the ourobouros

Symbol of human being

The human being, like the prism, is a Trinity. The three sides must be equal. In the same way, the human being must have harmoniously developed the triangle formed by his intellect, heart and will so that the light can manifest itself in all its splendor.

Only the equilateral triangle gives us the idea of perfect harmony because it expresses the agreement between the three principles where none has developed at the expense of the others.


The third principle

The triangle, we can say that it is the masculine and feminine principles that unite to give birth to a third principle. In the family it is father, mother and child; in chemistry, acid, base and salt; in man, intellect, heart and will (or thought, feeling and action), and among the divine virtues, wisdom, love and truth ... Just as a child is the product of a father and a mother, so salt is the product of acid and base, action is that of thought and feeling, truth is that of love and wisdom.

>> Go to the Idea Matrix

Alone, the equilateral triangle gives you the idea of perfect harmony, because it expresses the agreement between the three principles: none has developed at the expense of the others. If the equilateral triangle is the symbol of a perfectly balanced man, it is because it expresses precisely this agreement between the three principles of intellect, heart and will.

Triangle in Psychology

Connecting above and below

The drama triangle is a social model of human interaction – the triangle maps a type of destructive interaction that can occur among people in conflict. The drama triangle model is a tool used in psychotherapy, specifically transactional analysis. The triangle of actors in the drama are persecutors, victims and rescuers.


The Karpman triangle

  1. The Victim: The Victim's stance is "Poor me!" The Victim feels victimized, oppressed, helpless, hopeless, powerless, ashamed, and seems unable to make decisions, solve problems, take pleasure in life, or achieve insight. The Victim, if not being persecuted, will seek out a Persecutor and also a Rescuer who will save the day but also perpetuate the Victim's negative feelings.
  2. The Rescuer: The rescuer's line is "Let me help you." A classic enabler, the Rescuer feels guilty if they don't go to the rescue. Yet their rescuing has negative effects: It keeps the Victim dependent and gives the Victim permission to fail. The rewards derived from this rescue role are that the focus is taken off of the rescuer. When they focus their energy on someone else, it enables them to ignore their own anxiety and issues. This rescue role is also pivotal because their actual primary interest is really an avoidance of their own problems disguised as concern for the victim’s needs.
  3. The Persecutor: (a.k.a. Villain) The Persecutor insists, "It's all your fault." The Persecutor is controlling, blaming, critical, oppressive, angry, authoritarian, rigid, and superior.

Triangle in Philosophy and Spirituality

The Holy Spirit - The ternary law - The Three Worlds

The Three Persons and Holy Spirit

Vision of Trinity

The Christian Doctrine of the Trinity is in perfect harmony with other religions, as far as the role played by each of the Divine Persons is concerned. The word Person comes from persona (a mask, that which covers an object), and means the mask of the One Existence, the way in which He reveals Himself in a form. The Father is the Origin and the End of everything; the Son is double in nature. He is the Word, or Wisdom. The Holy Spirit is the Creative Intelligence which, hovering over the chaos of primordial matter, makes it fit to serve in the making of forms.


the three persons

The triangle, associated with the number 3, also represents the universal triple force of the Holy Spirit symbolized by the three Elements that serve to characterize it in the Bible: Fire, Air and Water.

Associated with the Holy Spirit is the model of the active force used by the Creator to initiate His creation. He is the original Source of all that lives and is created in the Universe, in all dimensions of space and time.

archetype shape of triangle

The ternary constitution of Man

Mind, Heart and Will

Most of the time, men/women are triangles with unequal sides. Some have a much more developed will, which means that in most cases they are content to carry out the projects of others.

Others, on the contrary, have the intellect and the heart much more developed than the will: this means that these people think and analyze a lot, that they are also very sensitive, but when it comes to acting, realizing, they expect others to do it for them.

When this triangle of heart, intellect and will is perfectly developed, man realizes Trinity inside him.

tree of three worlds

Man's triangle has its point facing down because it represents the cosmic Spirit that always descends towards matter, towards the earth, to vivify it, to spiritualize it and to give it a part of its energy: it represents involution. And the triangle of the woman has the point turned upwards because it is the symbol of the matter that goes up to reach its beloved, the spirit: it is evolution.

This meeting of spirit and matter is symbolized by the seal of Solomon, also called the hexagram.

« The ternary division is the most general and at the same time the simplest that can be established to define the constitution of a living being, and in particular that of man, because it is well understood that the Cartesian duality of "spirit" and "body", which has somehow imposed itself on all modern Western thought, can in no way correspond to reality.  »

René Guénon

The Plato's vision of World

A world made by triangles

This system of the World is based on the theory of Shapes or Ideas. These Ideas are, in his thought, the only real beings and the only ones that can be known, because they are eternal and immutable.

Form Plato the world is composed of assemblies of triangles, the four elements taken for simple bodies that transform into each other, a triple soul housed in three different places of the body.

Plato, takes the number, expressed by proportions and geometric figures, to make it the very basis of things, and since the triangle and the circle are the simplest and most perfect figures, he composes all the elements of triangles and gives the whole the spherical form.

« The constitution of living beings has indeed regulated life times for the whole species, and each individual is born with a life time fixed by destiny, apart from the inevitable accidents, because, from the birth of each one, his triangles are constituted in such a way as to be able to hold out until a certain time, beyond which no one can prolong his life. »  »

Plato - The Timeaus

Triangle is everywhere

The Mental Body

The art of proportion

The segment of a straight line determined by two points is in geometry, mechanics, architecture, the simplest element to which one can apply the ideas of measurement, comparison, ratio; the simplest operation introducing these concepts is the choice of any third point on this line; one passes from unity to duality and one is immediately in front of "proportion".

A proportion is the relation, the quantitative comparison between two quantities of the same nature, or the number that expresses this comparison. A proportion results from the agreement or equivalence of two or more ratios; therefore at least three quantities (here the line and its two segments) are needed to determine a proportion.

divine proportion

The proportion defined by a and b is called "extreme and medium reason" when a is to b what a + b is to a, i.e.: when (a + b)/a = a/b. The ratio a/b is then equal to the golden ratio.

« But it is impossible to combine two things well without a third: there must be a link between them. There is no better bond than that which of itself and of the things it unites makes one and the same whole. Now, such is the nature of proportion... »

Plato, Timaeus.

The basis of the reasoning

The syllogism is composed of three propositions. The first two are the premises, the last one the conclusion. It consists of three terms (here "man" (A), "mortals" (B) and "Socrates" (C))

  • Men are mortal,
  • Socrates is a man,
  • so Socrates is mortal.

If all A is B and all C is A, then all C is B.

This is the eternal basis of any possible reasoning or calculation, and therefore of logic and geometry.

For Aristotle, the syllogism is identified with deduction (which goes from the general to the particular), as opposed to induction (which goes from the particular to the general) and analogy (which goes from the particular to the particular).


The language of grammar

It is impossible to express a thought without forming what grammarians call a proposition. A proposition necessarily consists of three terms: the subject, the verb, and the attribute or adjective.

The verb that is active, powerful, and that makes the link. The whole grammar is based on these three functions, which we can also see in the triangle symbol.

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