The special energy of pythagorean pyramids

1.- Introduction

Until recently, my measurements of subtle energy over pyramid miniatures were limited to a skeleton of the Great Pyramid, and a tetrahedron and a regular semi-octahedron. In all cases, an emission of Negative Green in Electric mode (V-E) shape waves was observed through the apex. This was accompanied by a negative vital component, which is equivalent to what Wilhelm Reich referred to as DOR energy or Deadly Orgone Radiation. In the skeleton of the Great Pyramid, this harmful V-E emission was also present in the perpendicular of each base side. This means that, if we have such a skeleton at home, it will be continously emitting damaging energy to the environment. On the other hand, at the pyramid's inner vertical, a Negative Green in Magnetic mode (V-M) shape wave can be measured, approximatelly at 1/3 of its height. This one is beneficial to health (see the properties of this colour in reference [1]) and it comes accompanied by a positive vital component (orgone energy) (Figure 1).

Instrumentos de trabajo
Figure 1: Shape waves emission measured on a squeleton of the Great Pyramid built to scale: a Negative Green in Electric mode (V-E) shape wave is observed to the perpendicular of each base side, as well as through the apex, which comes accompanied by a negative vital component (DOR energy). In the inside, a Negative Green in Magnetic mode (V-M) is measured at approximatelly 1/3 of its heigh.


In light of those observations, I could not stop asking myself ¿Are all pyramids emitting an V-E shape wave through their apex? With this question in mind, I recently came across the following description of how to use a very special pyramid for the purification of flower essences. In Chapter IX of the book “Flower essences and vibrational healing” written by Gurudas [2], several methods are suggested to “enhance the life force and stimulate the effects of flower essences. These amplification techniques are not essential, but clinical results improve with their use:

“The relationship of geometric patterns or shapes to consciousness is a very complex subject. Each geometric pattern has therapeutic power with the pyramid being the most important […] Pyramids, quartz crystals, and to a lesser extent lodestones, amplify thought and regenerate what they come into contact with. This is particularly so with any form of vibrational remedies.

Using a pyramid with quartz crystals and lodestone around it, as depicted in Figure 2, is a powerful way to amplify flower essences. The base angles of the pyramid should be 62 degrees. One angle of the pyramid should be pointed toward magnetic north. This properly aligns the pyramid with the earth's magnetic energies.

The best material to use in constructing a pyramid is gold and then silver, but because these are expensive, copper, the third best metal, is usually suggested. Other metals and even wood can be used, but they would not work so well. Aluminum or plastic should never be used because they are toxic to health.

The actual size of the pyramid can generally vary depending on preference and what is to go under it; however, a base of eight inches as a minimum is best. In constructing a pyramid, if glue is used, only a natural non-chemical glue such as silica glue should be used. The pyramid can be fully enclosed or be skeletal in design.

Quartz crystal is a crystalline form of the element silica […] White or clear quartz is the purest and most powerful kind. For this work use quartz that is clear, geometrically proportioned, and one-pointed, instead of several small clusters. Place quartz by the pyramid's four sides. Small pieces of lodestone may be placed by the four angles of the pyramid in the shape of a horseshoe. It is best that only the positive and negative lodestones face each other. While it is wise to use lodestone, if one does not, the quartz pieces should be placed by the angles instead of along the four sides.”


Instrumentos de trabajo
Figure 2: Reproduction of Gurudas diagram about the use of a pyramid to purify and enhance the effect of flower essences. The effect of the pyramid is amplified by placing one-pointed clear quartzs in each base side, and a lodestone in each corner. The optimum slant suggested for the pyramid sides is 62 degrees [2].


After reading these lines, the first that I did was to add quartz cristals and lodestones to the dodecahedra that energise and purify our food and liquids at home. But inmediatelly after I started wondering: ¿Why using a basde angle of 62 degrees, instead of the 51.8 degrees of the Great Pyramid? So I got on with building a pyramid skeleton of those proportions to measure its energy. 

In what follows I will show you how the dimensions of this pyramid are directly related to exact pythagorean triangles, how this changes the energy inside and outwards the pyramid, and which other proportions could be optimum to enhance this effect.

2.- The energy of the 62o pyramid

To build this pyramid skeleton while being able to try out several proportions, using "pincho" wooden sticks and mouldable rubber adhesive came to my mind. The measurement of the physical component of shape waves was carried out with the Universal Pendulum. To measure the subtle components (vital and spiritual) a hebrew pendulum can be used, as described in the previous article. But on this occasion I used a neutral pendulum (Figure 3):

Instrumentos de trabajo
Figure 3: Working instruments used to carry on this research: on the left, the wooden neutral pendulum, with the knots suggested by Jean de la Foye [3, p.68] for measuring the subtle components of shape waves; on the right, the Universal Pendulum; and in the middle, the wooden sticks and the mouldable rubber adhesive.


Following the guidelines of Jean de la Foye [3, p.68], if we make three "stopping" knots, the phyisical, vital and spiritual components can be measured by holding the pendulum from each of those knots (Figure 4). Whem the pendulum turns in the opposite sense, the component being measured is harmful: for example, if this pendulum turns the opposite in the "vital" knot, we are being exposed to an Deadly Orgone Radiation (DOR).



Figure 4: A neutral pendulum with three stopping knots allows to measure the three subtle components of shape waves: physical, vital and spiritual. This method is equivalent to using the hebrew pendulum as described in our previous article (figures reproduced from [3]).


The following figure shows comparatively the skeletons we built of the Great Pyramid, the 62 degrees pyramid, and the 67.38 degrees pythagorean pyramid:

maquetas de la gran piramide y dos piramides pitagoricas
Figure 5: Skeletons of the 62 degrees pyramid (middle), the Great Pyramid (right), and the 67.38 degrees pythagorean pyramid (left). 


After conducting the measurements on the 62 degrees pyramid, the result are shown in Figure 6: on the one hand, we observe that the shape wave emission from the apex and the base sides is no longer harmful, and it combines the colours Violet (V) and Positive Green (V+). And on the other hand, this same kind of energy is concentrated in the inner vertical of the pyramid at two approximately equidistant heights. In addition, the vital and spiritual components are also present in all cases.

Instrumentos de trabajo
Figure 6: Shape wave emission measured on a skeleton of the 62 degrees slant pyramid: positive vital energy through the apex and all base sides, with physical components Violet (V) and Positive Gren (V+). The same energy seems to also concentrate at two approximately equidistant points of the inner vertical. As we will see later on, this energy seems to be produced in those pyramids that contain an exact pythagorean triple, which I call pythagorean pyramids.


The therapeutical properties of the shape waves of Positive Green and Violet colour are the following [1]:


- It’s the colour of protection par excellence, because it seals, regenerates and protects.
- At the physical level, it’s a regenerating and relaxing colour.
- It relaxes the thought.
- It helps with any kind of emotional or mental transmutation: it breaks old structures of thoughts and supports mental reorganisation.

Positive Green:

- It’s a cleaning colour.
- At the physical level, it’s suitable to treat the heart and the circulatory system.
- It relaxes the central nervous system.
- At the physical level, it acts by disinfecting and removing parasites. It is ideal to remove bacteria and fungi […] also applicable in case of virus and infections.
- At the emotional level, it releases conscious pain.

In view of the surprising change in the energetic properties of the 62 pyramid skeleton, as compared to the Great Pyramid's (slant of 51.83 deg), I asked to myself ¿what can be so special in those 62 degrees slant? After going again over the calculations made for building this pyramid, I realised that one of its right-angled triangles had approximately integer dimensions (Figure 7):

triángulo pitagórico casi exacto en la pirámide de 62 grados
Figure 7: In the 62 degrees pyramid, the right-angled triangle formed by its apothem and heigh has approximately integer dimensions. 

This observation made me think: ¿might other pyramids with an exact pythagorean triple share these same energetic properties? ¿And must the pythagorean triple necessarily appear in that specific triangle of the pyramid? ¡Let's find out!

3.- Pythagorean pyramids

Until now, I only knew that the pythagorean triangle 3-4-5 had special energetic properties, similar to the golden triangle ones: throughout its vertical it emits a Positive Green shape wave, accompanied by vital and spiritual components. The current research led me to try other pythagorean triples, and it seems that this property generalises to all of them. Figure 8 shows some of the pythagorean triangles that I have measured and fulfill it. All of them come from the first 16 primitive pythagorean triples, those whose sides are relative prime among them.

triángulo pitagórico casi exacto en la pirámide de 62 grados
Figure 8: Some pythagorean right-angled triangles, built with primitive pythagorean triples. It should be pointed out that their dimensions need not be integer values in cm. In fact, if we were using another measuring unit such as the inch, its translation to centimetres would not be an exact integer, but its properties would be the same. What has to be kept is the proportion between the three sides, as indicated by each triple.


A pythagorean pyramid can be defined as that which contains an exact pythagorean triple in some of its three right-angled triangles (Figure 9): the one formed by the edge c and the height h (T1); the one formed by the apothem a and the height h (T2), and the one formed by the edge c and the apothem a (T3):







Figure 9: (a) Characteristic dimensions of a square-based pyramid; (b-d) the three distinct right-angled triangles rectángulos it contains.


The formulae that allow for calculating the ratio between the edge c and the base side 2b for each of the three cases, as well as the slant angle α, are:

cálculo de la relación arista / lado de la base para un terna pitagórica
Figure 10: Formulae to calculate the ratio between the edge c and the base side 2b for each of the three right-angled triangles T1, T2 and T3 in a pyramid, as well as the slant angle α.


For this study, I wrote down the first 16 primitive pithagorean triples (m,n,p) with hypotenuse p<100, and I calculated the required ratio between the edge c and the base side 2b, as well as the corresponding slant angle α, depending on the triangle in which the pythagorean triple was located: T1, T2 or T3. The result is shown in Table 1:

medidas de pirámides con una terna pitagóricas primitiva en alguno de sus triángulos rectángulos

Table 1: Ratio between the base side 2b and the edge c in the pyramid, and the corresponding slant angle α, for the first 16 primitive pythagorean triples, assuming that the triple appears in triangle T1 (first two columns), triangle T2 (following two columns) or triangle T3 (last columns to the right). The first remarkable thing is that the 62.06 degrees pyramid has the basic pythagorean triple 3-4-5 in triangle T1!!

This table allows for calculating the dimensions of the base side, given the edge length, if one wants to build any of these pythagorean pyramids. For instance, to build the pyramid with slant α = 51.521 degrees, which has the pythagorean triple (28,45,53) in triangle T3, with an edge length c = 33.5 cm of my wooden stick, a base side length of 2b = 33,5 x 1,057 = 35,409 cm is required. Or just the opposite, if we want to fix the base side length, for example 2b = 30 cm, the table allows to calculate the corresponding edge length, which in the same example would be c = 30/1,057 = 28,38 cm.

Looking closer at Table 1, I had an enormous surprise when realising that ¡¡jthe 62.06 degrees slant was precisely giving a pythagorean triple 3-4-5 in triangle T1!! This would explain the properties of the 62 degrees pyramid that I had built following Gurudas suggestion in his flower essences book. The difference of 0.06 degrees with the exact figure of 62.06 shown in the table does not seem to destroy the energetic resonance that the pythagorean triple originates: we can observe that a pyramid with a slant of 62.00 degrees still approximates the triangle 3-4-5 very well (Figure 11):

triángulo pitagórico 3-4-5 en la pirámide de 62 grados
Figura 11: In the 62 degrees pyramid, the pythagorean triple (3,4,5) is very well approximated in triangle T1. 

In addition, Table 1 also shows that at slant angle of 61.93 degrees, a pythagorean triple appears in triangle T2, as we had observed approximately in the 62 degrees pyramid. And with an angle of 62.126 degrees, a pythagorean triple appears in triangle T3. This can be better appreciated is we sort the results for increasing values of the slant angle:

medidas de pirámides con una terna pitagóricas primitiva en alguno de sus triángulos rectángulos

Table 2: Ratio between the base side and the pyramid edge, sorted by increasing slant angle, for the first 16 pytagorean triples located in triangle T1, T2 or T3.

The conclusion is that around a slant of 62 degrees, a tenth of degree above or below, three very different pythagorean triples are produced. Perhaps this is the reason why Gurudas recommends using 62 degrees, because a small construction error might not destroy the desired energetic properties. However, we will see later on another case where some tenths of degree make a complete change in the pyramid's energy.

To determine whether the energetic properties of the 62 degrees pyramid were mantained in all other pythagorean triples, I measured some of those triples in the previous tables, placing them in different possible triangles of the pyramid (T1, T2 or T3). To do so without having to build all the pyramids, I used the same set of edges, while drawing the base square for each case on a peace of paper, according to the proportions in Tables 1 and 2 (Figure 12). Then I observed the following:

- For all the cases that I tested, the same energy emission as in the 62 degrees pyramid is observed: Positive Green and Violet with vital and spiritual components, both through the apex as well as through the four base sides, and at two approximately equidistant points in the inner vertical of the pyramid. I could not determine if the effect was more intense when the pythagorean triple was located in triangle T1, T2 or T3, but in all three cases the same energy type is present.

- When moving the edge tips to a slightly smaller or bigger square than the one marked on the paper, the energy emission produced by the exact pythagorean triple is completely lost, and the pyramid goes over to emitting Negative Green in Electric mode with negative vital energy from its apex.




Figure 12: Measuring the (a) physical, (b) vital and (c) spiritual components of the shape waves produced by one of the pithagorean pyramids. When slightly moving the edge tips outside or insde of the base square, this energy stops being emited.

In Table 2 the 67.38 degrees pyramid also stands out (Figure 5, left), because two pythagorean triples happen to meet in it with great accuracy. My feeling was that in this case the penduli turned with a greater intensity. Asking with the neutral pendulum, I got an energy of 48.000 Bovis in the 62 degrees pyramid, against 55.000 Bovis in the 67.38 degrees one. It would be very interesting if somebody could confirm those findings.

Another curious case is the 51.521 degrees pythagorean pyramid, which has a very close slant to the 51.83 degrees of the Great Pyramid. After measuring this pyramid, I could check that it effectively had the expected emission for a pythagorean pyramid, and that slightly moving the edge tips to the interior of the square until reaching the proportions of the Great Pyramid, the energetic properties changed completely to the expected for the latter one. For an edge length of c = 33.5 cm, the difference in base side length between those two pyramids is only 2 mm, but with this small change ¡¡the energetic properties of the pyramid change as day to night!!

Finally, it is also remarkable the 53.894 degrees pyramid, which has the edge to base ratio 2b/c = 1.015 closest to unity (that is, to a perfect semi-octahedron). For an edge length c = 33.5 cm, the corresponding base side length is 34.00 cm. When measuring this other pyramid, I found again the same properties of the 62 degrees pyramid. That means that, going away only half a centimeter from a perfect semi-octahedron, we switch from a harmful shape radiation with Negative Green in electric mode through the apex, to a highly beneficial shape radiation of Positive Green and Violet colours, accompanied by the positive vital and spiritual components, both in the inside and outwards from the pyramid (Figure 6).

4. Conclusions

The results of this small investigation suggest that the pyramidal shape is actually a highly sophisticated resonant instrument, that concentrates and scatters subtle energy at several levels. A small change in the proportions of a pyramid, turning it into a pythagorean pyramid, makes it change from emitting a shape wave that is damaging to our health and environment, into emitting a completely different shape wave that is highly beneficial for life. In addition, there are specific dimensions, such as the slant angle of 67.38 degrees, that seem to concentrate and emit this energy in an even more intense way, because two pythagorean triples happen to coincide in it at the same time.

These results may have many applications. For example, pyramidal shaped orgonites would amplify their effect were pythagorean pyramid dimensions used for their construction. Having such a pyramid skeleton near us can help to balance and purify the environment, as well as everything that is placed inside it. As suggested by Gurudas, the effect of a pyramid can be amplified by putting a lodestone at each corner and a point-shaped white or clear quartz at each base side. A pythagorean pyramid of natural size, in addition to enormously harmonizing the environment around it, could also be used as a therapeutical instrument, putting a person inside it to rebalance his/her energetic bodies.

Last update: 2022/08/24


5. References

[1] Adreiñua de Santiago, Elena: "El Péndulo Universal: Guía práctica de uso y aplicación", Ed. Hakabooks, Barcelona, 2018.

[2] Gurudas: "Flower Essences and Vibrational Healing", Cassandra Press, San Rafael, CA, 1989.

[3] De la Foye, Jean: "Ondes de vie, Ondes de mort", Ed. Robert Laffont, Paris, 1975.