The familiar Pythagorean Theorem is essentially the expression of a general law of life.
It shows in a geometric way how, on the basis of the masculine principle, the three, and the feminine principle, the four – as thesis and antithesis interrelated by a right angle (conscious distinction) – the synthesis is generated. This may be seen as the “child principle”. This “child” links the parents with each other; it is the hypotenuse.
The right-angled triangle with three and four as the two short sides and with five as the hypotenuse is sometimes called the golden triangle. The three, expressing as we said before, the concept of man, the masculine principle (spirit, mind, energy …) is perfected in the square of the three, the highest that is possible in the world of the three:
It is the fulfilment of the masculine principle.
The four, by which geometry expresses the concept of woman or the feminine principle (intuition, surrender …), is perfected in the square of the four, the highest that is possible in the world of the four:
It is the fulfilment of the feminine principle.
If man and woman as a unity achieve the highest, the utmost, of what they are able to achieve, they will join as
32 + 42 = 52 or 9 + 16 = 25
Then twenty-five is the square of the five, the fulfilment of the five. This is the desired fruit, the manifestation, the child. It is the fruit of man and woman, when both have become a unity, both fulfilling him or herself. Thus the new is born.
The cross-section triangle of the Chefren pyramid in Egypt consists of two golden triangles, the short sides of which form a right angle and have the proportion three to four. The hypotenuse, representing the five, leads upwards to the top of the pyramid.
In the image of the pyramid as well as in the Pythagorean Theorem, the path assigned as a task to human life unfolds. It is a path that leads out of material attachment to the world of the four into the world of the spirit.
In general, the top of any pyramid with a square as its basis, forms the five. From the square, the fifth point, the top of the pyramid, the quintessence arises above its centre.
The manifested, material world of the four needs an opposite pole that has been generated from it; it needs a consciousness that is able to understand that system and order also rule the earthly world, a consciousness that develops according to soul and spiritual laws. This opposite pole is the human being, the five, that moves perpendicular to the earth. It is the justification; it is conceived as an organ to recognise God. We can see his task in the symbolism of the pyramid.
The human being develops from the four. We can imagine this symbolically, if he stands upright on the earth and spreads his arms. Then he forms a cross. It is his task to mediate between the concrete, earthly world (the horizontal axis) and the divine primordial ground (the vertical axis) and to overcome the opposites. Just as a person, when he is standing, occupies his place between heaven and earth, the five occupies the central position in the range of numbers 1-9.
It is situated in the middle of the arc of tension between heaven and earth:
In addition, five is the sum of two – the polarity in matter – and three – the victory over the division in the divine power.
2 + 3 = 5
In the Hebrew and Indian cultures, the five expresses the creative human will and his indwelling, individual powers. The five is indivisible. We may see this as a reference to the individuality, to the indivisible in the human being. Through the link of two and three, we become conscious of this. If a human being has matured by experience, he is able to ascend from what is primitive individual to what is Creative individual, the perfection of the five.
This mystery becomes clear, when we take a closer look at the geometric figures, belonging to the five, the pentagon and the five-pointed star (pentagram).
The pentagram was so strongly worshipped as a holy sign that its construction was kept secret until the sixteenth Century. Of old, it was a symbol of the divine order. Without the circle (the symbol of unity) and the cross (that is its cross-section), it cannot be constructed. The relationship between pentagram, circle and cross symbolises the path, to which seeking man is called. The way out of the world of the four is made possible for him by surrendering his whole life to the world of the one. In this context, the soul is transformed into a pentagram.
If we look at the pentagon, a link with infinity might be suggested by the following construction: From one angle, for instance the top one, we can construct a series of pentagons or pentagrams that, mutually linked, become ever-smaller and grow towards the upper angle that links them. Conversely, however, it also seems as if ever more pentagons and pentagrams grow outward ad infinitum. In this way, we can imagine that the smallest pentagon is a symbol of the microcosm, in which the secrets of the macrocosm are reflected.
Likewise we can recognize that also inside each pentagram there is a pentagon in which a pentagram can be constructed etc. Thus the pentagram is a symbol for man who is embedded in the cosmic whole.
The pentagram contains still another secret: that of the golden section or divine proportion. The human limbs, too, have these proportions in a normal figure: with outstretched arms, the proportion of the length of the arm to the width of the shoulders plus the length of the arm is that of the golden section. The same is true for all other limbs of the human body: hands, fingers, toes, legs, head and trunk.
This coherence symbolises that there is a Separation from the whole, but the separated part still remains linked with the whole.
During the Middle Ages, in the Cabbala of Heinrich Cornelius Agrippa, we already find the figure of the human body with outstretched arms and legs represented as a pentagram.
Man is called to freedom and possesses the body as an instrument that shows the laws of divine division. We can see this particularly in his limbs. They serve his actions.
If a person walks the path of becoming conscious, he will also gain more power by his increasing knowledge, and his freedom and independence will grow. Such an individual can always choose to use his freedom in two ways.
We also know two ways to represent the pentagram: either with one point upward or with two points upward. The latter refers to the duality and is often associated with the evil one, with the two-horned devil, the fallen angel.
Thus, the described way from the one to the five contains the beginning of the process of becoming conscious, the steps of perception, crisis, decision, and thus the attained insight into things, the knowledge of the purpose. In addition, this path implies a continuous deepening and purification in the material world by recognising the opposites and the transience of everything earthly. This is why the way leads inward, to the spiritual principle in the heart.
In this way, the five rises up from the four. If a human being recognises, on the basis of the sum of his experiences and the related purifications, the principles according to which life has been formed, he will in his fifth stage begin to actually and consciously lead his life according to spiritual laws. Thus he begins his path of initiation, the inner rebirth from the Spirit, from the spark of the Spirit in the heart.
If we consider the geometric origin of the pentagon, we can also recognise this path in the sober symbols of this geometry.