The Egyptian Triangle 3-4-5
When gematria and sacred geometry meet, a divine language
The Egyptian Triangle 3-4-5 is an interesting triangle that carries deep esoteric significance. The area of the circle inscribed in the triangle equals precisely the number π (3.14). This remarkable relationship hints at a deeper symbolic understanding of geometry as a bridge between the finite and the infinite, the measurable and the transcendent. Part of their thought in ancient Egypt was that π was not a number but a symbol of cosmic order, the cyclical nature of existence, the eternal nature of being, and the infinite wisdom in creation. The latter signifies wholeness and unity and brings us to the key to the mysteries of the universe as defined by π.
According to the Kabbala, the entire creation began as a perfect circle. God "constricted" His infinite light into a perfect circle to make room for the creation. Pi (π) was used to bring this circle (Tzimtzum) wholly and perfectly. In the words of the sixteenth-century Safed Kabbalist R. Isaac Luria:
Before the emanated beings were emanated and the created beings created, a lofty, undifferentiated light filled all existence, and there was no cleared space… That [light] is called the Light of the Infinite (’ôr ’ên sof). When it arose in His undifferentiated will to create worlds… He then constricted Himself, the Infinite, at His core point… and He constricted that light, and it was distanced to the sides surrounding the middle point. Then there remained a cleared space and an empty atmosphere and hollowness… Then there was a place in which beings could be emanated and created… (‘Ēṣ ḥayyim, 1:2)
Sacred geometry, as naturally embedded in the 3-4-5 triangle, is the perfect example of how mathematics was once regarded as a divine language meant to decipher the harmonious intermingling of physical structures from those metaphysical principles of which they were composed.
Plutarch first describes the Egyptian 3-4-5 triangle in Moralia Vol. V:
“The upright, therefore, may be likened to the male, the base to the female, and the hypotenuse to the child of both, and so Ausar [Osiris] may be regarded as the origin, Auset [Isis] as the recipient, and Heru [Horus] as perfected result.”
The short side of the right-angle triangle is named “Ausar,” which corresponds to Osiris, the Father. The longer side is named “Auset,” corresponding to Isis, the Mother. And finally, the hypotenuse is called “Heru,” or Horus, the Son.
The ancient Egyptians saw this geometric figure as the prime matter or the One Substance that contains everything—all the elements that make matter and stages of consciousness1.
The 47th problem of Euclid.
The Pythagorean triangle 3-4-5 is a geometric figure representing the universal harmony in the microcosm and macrocosm. As above, so below. The human being is a mirror of the eternal creative energy, the pure light of the nondual Spirit. Each triangle is attributed to each principle of the three-ness, a trinity well known in Ancient Egypt as Osiris, Isis, and Horus the child.
Osiris is the triangle of edge length 3, representing the three vital principles: salt, sulphur, and mercury.
Isis is the triangle 4, which was the expression of the four basic elements: fire, water, air, and earth.
Horus the child, the body (salt) incarnates the nondual spirit through the union process between the father and the mother. The Father, passing his vital principle through the mother, continues to live in the child. Horus represents the five stages of the development of life: minerals, plants, animals, humans, and enlightened ones.
The Theorem of Pythagoras speaks about this beautiful process within:
As Plutarch describes:
“Three is the first perfect odd number: four is a square whose side is the even number two; but five is in some ways like to its father, and in some ways like to its mother, being made up of three and two. And panta, (all), is a derivative of pente (five), and they speak of counting as ‘numbering by fives.’ Five makes a square of itself.”
In this particular triangle, the segment [AK] represents the descent of pure light (spirit) into matter and has a side length equal to 7.4. It is the line of balance between the triad, passing through the right angle A and extending perpendicularly to the side [BC] and then to the side [ED]. Interestingly, the angle SAR, which can be seen as the light cone projected, is about 37 degrees. If we had to break the light cone projected into two parts with the angles SAJ (23.385 degrees) and JAR (13.671 degrees), the latter would be about 37% of the original angle SAR (37.057 degrees). So, the prime number 37 seems to be a central key number in the Egyptian Triangle 3-4-5.
The angle SAJ could refer to the precession angle of Earth, approximately valued at 23.4 degrees.
The side length [AK] equal to 7.4 is a numerical code well encoded in the Bible, particularly in the first verse of Genesis. The expanded form of this verse in Hebrew Gematria is 5476 (using the Mispar Shemi Method). The first verse can be written in its expanded form, and the total sum of the Hebrew letters is the square of 74, which is 5476. For example, Alef is 111, and the numerical value of its full name is: אלף = 100 + 10 + 1 = 111.
First verse:
בראשית ברא אלהים את השמים ואת הארץ׃ = 5476
The first verse in its expanded form (full standard):
בראשית = 1819
1033 = ברא
291 = אלהים
517 = את
546 = השמים
ואת = 539
731 = הארץ׃
The number 74 is also the standard gematria value of Jesus in English.
J = 10
E = 5
S = 19
U = 21
S = 19
The number 74 is the numerical value associated with the central line (represented by the segment [AK] in our illustration) in the triangle 3-4-5, representing the stillness and equilibrium of every aspect of the divine creation. Further mention of this particular line in the next articles will be called the transcended line or the descent of light into the physical world. The first verse mentions, in the beginning, that Elohim created the heavens and the earth. No doubt it began with the number Pi (π), which is at the core of the universe because everything is composed of cycles that spin, orbit, rotate, or oscillate. Pi (π) defines all the cycles of the spinning and orbiting of atoms, planets, solar systems, galaxies, etc.
This article invites us to meditate upon a simple geometric figure that embodies the entire universe and the original coding of the number Pi (π) as the boundaries were defined for God’s creation.
Are we experiencing a simulation of an expanded universe that is already bounded by the parameter Pi (π) from the beginning? At the origin of the coding of such a wonderfully ordered cosmic play, we can dive in enough to start to see some of the important correlations between the words, geometry, and the alphabetical letters, either in Hebrew, Greek, English, or any other language. There is more to explore, which is the point of the Quantum Blueprint.
Triangle image and discussion from a description in Case, Esoteric Keys, 55.