Sri yantra, also known as Sri Chakra, is called the mother of all yantras because all other yantras derive from it. In its three dimensional forms Sri Yantra is said to represent Mount Meru, the cosmic mountain at the center of the universe.

The Sri Yantra representation of the cosmos at the macrocosmic level and of the human body at the microcosmic level (each of the circuits correspond to a chakra or vortex  of the body).

The Sri Yantra is a configuration of nine interlocking triangles ( 9×9 grid or gross body ), surrounded by two circles of lotus petals with the whole encased within a gated frame, called the “earth citadel”. The nine interlocking triangles centered around the bindu (8×8 grid the central point of the yantra or microabode or subtle body ) are drawn by the superimposition of five downward pointing triangles, representing Shakti ; the female principle and four upright triangles, representing Shiva ; the male principle. The nine interlocking triangles form forty three small triangles each housing a presiding deity associated with particular aspects of existence.

Man’s spiritual journey from the stage of material existence to ultimate enlightenment is mapped on the Sri Yantra. The spiritual journey is taken as a pilgrimage in which every step is an ascent to the center (8×8) , a movement beyond one’s limited existence, and every level is nearer to the goal. Such a journey is mapped in stages, and each of these stages corresponds with one of the circuits of which the Sri Yantra is composed from the outer plane ( 9×9 ) to the bindu ( 8×8 ) in the center.

The Sri Yantra is a tool to give a vision of the totality of existence, so that the adept may internalize its symbols for the ultimate realization of his unity with the cosmos.

The goal of contemplating the Sri Yantra is that the adept can rediscover his primordial sources. The circuits symbolically indicate the successive phases in the process of becoming.

Nine Triangles in a Circle

Four triangles pointing up.
Five triangles pointing down
Central figure
Complete Sri Yantra
Figure 1

The Sri Yantra is composed of a central figure that is surrounded by two circular rows of petals and then by a rectangular enclosure called the bhupura. In this blog we will be focusing mainly on the central figure which is composed of nine overlapping triangles and a bindu point. Four of the triangles point up, the other five point down. In the most popular configuration the two biggest triangles (green triangles in figure 1) touch the outer circle on all three points.

Concurrent Interconnections

sri yantra marmas
Figure 2
Triple intersections.

When looking at the figure we notice that there is a high degree of interconnectedness between the nine triangles. This means that every triangle is connected to one or more of the other triangles via common points and they do not criss cross .

Figure 2 shows where the triple intersection points are located. These are the points that lock together the triangles. You can’t move one without also moving the others. This interconnections scale up to infinite small ( Planck length , protons et  ) to infinite big ( cosmos , universe ) .This is the principle of cosmic entanglement .

Notice also that the two biggest triangles are touching the outside circle on three points and that the apex of every triangle is connected to the base of another triangle.

The up and down triangles when overlapped give a pentacle . Thus Sri Yantra is a geometry with five degrees of freedom ( pentadic scale of cosmic regulation called panchmahabhuta in Hinduism and 5 energies in Chinese occult ) , which means that up to five different criterion can be used to define it. This is why we have to decide on the location of five lines when drawing the figure. Five degrees of freedom is not a lot considering that there is a total of nine triangles. This is because of the high degree of interconnectedness between the triangles. This effectively limits the possibilities and variations that can be achieved.

Concentricity :

Figure 3
Concentricity: the center of the innermost triangle coincide with the center of the outer circle.

Lets now take a look at the bindu point; the small point located in the central triangle. It should be located in the center of the innermost triangle. This can be achieved precisely by placing the bindu at the center of a circle that fits inside this triangle  . This is known in mathematics as the incenter of a triangle.

To achieve a perfectly centered figure however, the bindu should also be located at the center of the outer circle. This is illustrated in figure 3. The red cross shows where the center of the outer circle is located. The small red circle shows where the center of the innermost triangle is.

Equilateral Inner Triangle : 

geodesic dome
Figure 4
R. Buckminster Fuller stands in front of his geodesic dome.

The equilateral triangle is a perfect and minimal structure. It is the simplest, strongest and most fundamental structure in geometry and computer graphics. It has the highest degree of tensegrity for a minimum amount of structural elements. That is why it is so prevalent in the structural designs created by R Buckminster Fuller. This is also why the geodesic dome , a  spherical structure composed of small triangles is the only man-made structure that becomes proportionally stronger as it increases in size.

Figure 5
Equilateral triangle as the expression of Rishi, Devata, Chanda.

The Sri Yantra symbolizes, among other things the unfoldment of creation. The bindu represents the unmanifest ( 8×8 grid of subtle body ) , the silent state. The next level in the expression of the Universe is represented by the innermost triangle. This level represents the trinity of rishi, devata, chanda, or the observer, the process of observation and the object being observed. At this point the symmetry of creation is still intact and will be broken when it reaches the next level which represent the grosser aspects of the relative.

This reflects the unfoldment from unity or singularity to trinity as expounded in the Vedic literature. According to the Veda the Universe becomes manifest when unbounded awareness becomes aware of itself. The spark of self awareness ignites creation. At this point Unity divides into the trinity of rishi (the observer), devata (process of knowing) and chanda (the object of perception). The same idea is also found in the bible as the principle of the holy trinity.

The central triangle is the central lens of the Sri Yantra. If as some suggest, this pattern is capable of emitting a significant amount of subtle energy, the importance of having a well balanced and centered figure becomes obvious.

For these reasons the central triangle should be equilateral in an optimal . For this to happen the highest down pointing primary triangle must have an angle of 60 degrees .

 Center of Mass

 center of mass center of mass
Figure 6
Left: Figure with Concurrency criteria only. Center: Figure with Concurrency and concentricity. Right: Figure with Concurrency, concentricity and equilateral central triangle.

Another measure of overall balance of a structure is the center of mass. This is the point in the geometry where it would balance if it was a solid object.

Figure 6 shows a detail view of the central triangle of three different Sri Yantras. The left figure shows a configuration where only concurrency is achieved. In this case the bindu (red dot), the center of the outer circle (green dot) and the center of mass (blue dot) are not aligned.

The central figure shows a Sri Yantra that achieves concurrency and concentricity. As a result the bindu (red) and the center of the outer circle (green) overlap nicely. The center of mass still doesn’t overlap however.

On the right we see that for a figure drawn with the three criterion that we have suggested (concurrency, concentricity and equilateral central triangle), the three centers overlap and we have a perfectly centered and balanced figure where the bindu is well centered and more importantly the centermost triangle has an angle very close to 60 degrees. This is called perfect balance or harmony with the source of all existence .

Sri Yantra

Since the Sri Yantra is based on triangles it is very appropriate that there are currently three main ways to represent this figure. The first and probably the most common is the plane form, which is what we have been looking at so far.

The second is the pyramidal form called Meru   in India. Mount Meru is a mythical mountain. So named because of the mountain shape of the figure.

The third and rarest form is the spherical form or Kurma .  Kurma was the second incarnation of Vishnu, the turtle incarnation. This refers to the similarity between this form and the shell of a turtle. Ever wondered why the shell of a turtle is so robust . It is interesting to note that there seems to be some confusion with the use of these two terms. The pyramidal form is often wrongly referred to as Kurma.

Mathematics of Sri Yantra

A hymn from Atharvaveda is dedicated to an object that closely resembles this . The sriyantra (‘great object’) belongs to a class of devices used in meditation, mainly by those belonging to the Hindu tantric tradition. The diagram consists of nine interwoven isosceles triangles four point upwards, representing Sakti, the primordial female essence of dynamic energy, and five point downwards, representing Siva, the primordial male essence of static wisdom The triangles are arranged  in such a way that they produce 43 subsidiary triangles, at the centre of the smallest of which there is a big dot (known as the bindu). These smaller triangles are supposed to form the abodes of different gods, whose names are sometimes entered in their respective places. In common with many depictions of the sriyantra they have  outer rings consisting of an eight-petalled lotus, enclosed by a sixteen petalled lotus, girdled in turn by three circles, all enclosed in a square with four doors, one on each side. The square represents the boundaries within which the deities reside, protected from the chaos and disorder of the outside world.

Tantric tradition suggests that there are two ways of using the sriyantra for meditation. In the outward approach one begins by contemplating the bindu and proceeds outwards by stages to take in the smallest triangle in which it is enclosed, then the next two triangles, and so on, slowly expanding outwards through a sequence of shapes to the outer shapes in which the whole object is contained. This outward contemplation is associated with an evolutionary view of the development of the universe where, starting with primordial matter represented by the dot, the meditator concentrates on increasingly complex organisms, as indicated by increasingly complex shapes, until reaching the very boundaries of the universe from where escape is possible only through one of the four doors into chaos. The ‘inward’ approach to meditation, which starts from a circle and then moves inwards, is known in tantric literature as the process of destruction ( a falling blackhole and emerging by big bang in a new universe ) .

The mathematical interest in the sriyantra lies in the construction of the central nine triangles, which is a more difficult problem than might first appear. A line here may have three, four, five or six intersections with other lines. The problem is to construct a sriyantra in which all the intersections are correct and the vertices of the largest triangles fall on the circumference of the enclosing circle.

There is, however, a curious fact about all the correctly constructed sriyantras, whether enclosed in circles or in squares. In all such cases the base angle of the largest triangles is about 51. The monument that comes to mind when this angle is mentioned is the Great Pyramid at Gizeh in Egypt, built around 2600 bc. It is without doubt the most massive building ever to have been erected, having at least twice the volume and thirty times the mass of the Empire State Building in New York, and built from individual stones weighing up to 70 tonnes each. The slope of the face to the base (or the angle of inclination) of the Great Pyramid is 51�50’35.

It is possible from the dimensions of the Great Pyramid to derive probably the two most famous  numbers in mathematics. One is pi, and the other is phi the golden ratio   or ‘divine proportion’, given by (1 + sqr-rt 5)/2 (its value to five decimal places is 1.61803). The golden ratio has figured prominently in the history of mathematics, both as a semi-mystical quantity (Kepler suggested that it should be named the ‘divine proportion’) and for its practical applications in art and architecture, including the Parthenon at Athens and a number of other buildings of Classical Greece. In the Great Pyramid  the golden ratio is represented by the ratio of the length of the face (the slope height), inclined at an angle theta to the ground, to half the length of the side of the square base, equivalent to the secant of the angle theta. The original dimensions of the Great Pyramid are not known exactly, because later generations removed the outer limestone casing for building material, but as far as we can tell the above two lengths were about 186.4 and 115.2 metres respectively. The ratio of these lengths is, to five decimal places, l.618 06, in very close agreement with phi. The number phi has some remarkable mathematical properties. Its square is equal to itself plus one, while its reciprocal is itself minus one. But the most intriguing feature is its link with what are called the Fibonacci numbers.

The Fibonacci numbers are the sequence

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, …

where each number equals the sum of its two predecessors. This sequence pops up in a variety of natural phenomena – in pattems of plant growth and in the laws of Mendelian heredity, for example. It is easily shown that the ratio between successive Fibonacci numbers gets closer to phi the further up the sequence one goes. In the Fibonacci sequence given above, the ratio of 233 to 144 gives the value of phi calculated from the dimensions of the Great Pyramid.

The quantity pi can also be found in the dimensions of the Great Pyramid. If its height (1466 metres) is taken to be the radius of a circle, the perimeter of its base (4 x 230.4 = 921.6 metres) is almost equal to the circumference of that circle (2pir = 921.6 metres). The product of pi and the square root of phi is close to 4.

The largest isosceles triangle of the sriyantra design is one of the face triangles of the Great Pyramid in miniature, showing almost exactly the same relationship between pi and phi as in its larger counterpart.

Bolton and Macleod Sri Yantra

The term yantra, which literally means an instrument for holding or restraining, may be used to denote a variety of linear diagrams which play a significant role in the meditative practices of Tantric Hinduism. Yantras may be simple designs such as the cross, triangle, square, circle or lotus pattern, symbolizing basic concepts, or may be more complex combinations of such elements in figures representing in abstract form the particular creative forces in the cosmos which are called divinities. they are closely related to the mandalas used by both Hindu and Buddhist Tantrism, in which geometric design is supplemented by elaborate symbolic images of the deities which by their various forms and attributes indicate different aspects of the hidden order of reality. As Mircea Eliade says (1), the yantra is ‘the linear paradigm of the mandala’, expressing the same principles in geometric form. Like mandalas, yantras are used in the context of meditation and worship as visual-aids to concentration of the mind leading to realization of abstract principle which is the inner meaning of the visible representation.

The best known and geometrically the most complex yantra is the Sri-yantra, also known as the Sri-yantra . The structure of this yantra is enigmatically described in the Saundarya-lahari (The Wave of Beauty)  a lengthy poem praising the great goddess whose dwelling place the Sri-yantra is said to be .

By reason of the four Srikanthas (srikantha is an epithet of Siva) and the five damsels of Siva (which have the nature of Sakti), which are penetrated by Sambhu (i.e. bindu- the dot in the centre) and constitute the nine fundamental natures, the 43 (or 44) angles of your dwelling place are evolved, along with the 8-petalled and 16-petalled lotuses, the circles and the three lines.

The diagram may be more accurately described as a bilaterally symmetrical figure composed of nine interwoven isosceles triangles, usually depicted with five triangles pointing downwards and four pointing upwards. The former are said to correspond to the yoni representing the dynamic female principle of energy (Sakti), while the latter correspond to the linga representing the static male principle of wisdom (Siva). (The Buddhist Tantrics, incidentally, regard the male principle as dynamic and the female as static.) The central dot called bindu ( singularity ) represents the original unity of the male and female principles prior to creation and the paradoxical point female principles prior to creation and the paradoxical point from which the manifestation of the cosmos emerges. The interpenetration of the nine basic triangles gives rise to a number of subsidiary triangles (43 including the central triangle enclosing the bindu) which form the abodes of the deities, representing the particularization of the original creative forces into more concrete manifestations. Sometimes the names of deities and Sanskrit syllables are written into these triangles, or images of the deities are placed in them.

In most versions of the yantra this central design is enclosed by two circular lotus-patterns with eight and sixteen petals, a girdle of three concentric circles, and finally a square arrangement of straight line (‘the three lines’) with four openings or ‘doors’ at the cardinal points called ‘World House’ (bhugra). This square outline, which is common also to mandalas, symbolizes the royal palace in which the deities reside – an area of sacred space protected from the disintegrating forces of chaos. In general, the Sri-yantra is a ‘cosmogram’ – a graphic representation of the universal processes of emanation and reabsorption reduced to their essential outline. The yantra is an expression in terms of linear symbolism of the cosmic manifestations, beginning with the primordial unity.