Phi related construction.

This blog is about constructing the Sri Yantra. Not so much as a tool for meditation, there are a lot of  other good websites and video's available for that, but rather with focus on the geometrical aspects. (There are some other good websites for that as well, but i would rather  like you look at this one!)

There are some obstacles in drawing this diagram. And it is not allways easy to ceep track on where you are in the process. So it is important to make the whole construction as easy as possible.

The aim is then to find a construction method that is mnemonic; a method that is easy to remember. It doesn't matter if all the steps don't come to mind at once. As long as you have the basic information, you'll figure it out. Because after three steps, as you will see, the construction is fixed. All you have to do then is to connect the existing crossingpoints to find the next triangle.

Secondly, the less construction lines that needs to be drawn, the less chance there is that small errors cascade in to totall mess when drawing by hand.

Finally, it has to be correct. The triangles has to be arranged in the proper way obviously, but there are some esthetical rules to conscider as well.

Which brings us to the unavoidable error. No Sri Yantra is perfect. By definition. There are 18 coördinates where three lines have to meet and cross, nine on each half. There will be one on each half that doesn't meet exactly. But it is possible to make this error so small that it becomes irrelevant.

The Sri Yantra is not only the triangular arrangement. The rings, Lotus leaves and temple are just as important. Traditionally there are rules that govern their proportions, but it seems that this is of less importance in modern times.

The construction that is on display here is based on the Golden Mean. A specific proportion that plays a role everywhere and on every scale where nature manifests itself. As with the spiritual aspects of the Sri Yantra; there is a lott of good information on that available that doesn't need to be repeated here. It seems apropriate that a cosmogenic drawing takes the Golden mean as its fundamental principle though. it makes sense. Besides, we are hardwired to conscider this proportion as beautifull. So that helps to make the Sri Yantra more apealling.

A short introduction to give some cultural historic background is in order.

I do not claim to have any accurate knowledge on Hinduism or any other eastern religous- or philosphic body. I give this summary so that you can find out more if you wish to do so.

When contemplated negativly ( from the outside inward) it deals with the microcosmos, the psychological constitution of  Man. It is dedicated to Tripura Sundari, an aspect of Shakti.

When vieuwed positivly, from the centre outward, it is about the origin of the macrocosmos. Not only the physical universe, but allso the different etherical domains. Shiva and Shakti are behind the Bintu, the dot in the cente, and conceptuate 43 lesser deity's ( the smaller triangles), who in turn create the physical plane.

The vertical axis is actually an east-west line. The diagram can allso be seen as a callender. But i have no idea how that works.

It is assumed that the Sri Yantra is at least 5000 years old.

The construction of the temple, Lotus leaves and rings come in a later entry. For now i focus on the arrangement of triangles.

Start with a circle from centre A with radius A-B. Let's say that A-B = 100.

Construct vertical axis B-C, and horizontal axis D-E.

When drawing by hand, this may very well be the hardest part of the whole construction. A proper 90° angle is harder to draw than it seems, i have learned.

Determine midtpoint F on A-E and draw a circle with radius A-F = 50. Pythagoras' theorem will tell us that C-F, as in the triangle A-C-F is 111,803398875.. If segment C-F is extended to G, C-G is 161,803398875.. which is the greater part of the Golden Mean to A-B.

C-F is √5 of A-F.

Construct a semicircle from C with radius C-G and make that touch the big circle at H and I.

Construct triangle C-H-I. This is the biggest of the downpointing triangles. There are five downpointing triangles which are Feminine in nature, dedicated to Shakti. So i number them F1-5. The four up pointing triangles are dedicated to Shiva and represent the Masculine. They are numbered M1-4.

As you can see, the side of F1 is equal to segment C-G. So ɸ (Phi) related to the big circle.

(You may allready know this, but a segment B-H (not drawn) will be the side of a pentagon. Pentagonal shapes are the geometrical manifestation of ɸ. In other words, the base of F1 is the upper line of the arms of a pentagram as it would be drawn in the circle).

Draw a circle with radius A-J and copy that so that the top lies tangent with B.

Construct triangle B-L-M. This is triangle M1.

The ɸ proportions in this triangle are less obvious B-L: B-K = B-K: K-L = √ɸ. Or B-L+ B-M = ɸ M-L. But most of all A-B = ɸ A-J.

If this sounds familliar, you are correct. These are the same proportions as the Great Pyramid. Connecting two different cultures together with shared knowledg of ɸ, and π as well.

B-L = ¼ of the circumference of the circle that holds the Sri Yantra (99,9% accuracy).

it's a nice detail; the Feminine part is ɸ, beauty, growth, while the Masculine is π, containment, a powerstatement. Knowledge of π enabled kingdoms to build better and bigger. Showing a squared circle is a subtle way to show you'd not only the gods on your side, you knew how to use their powers as well!

We'll return to the construction of ɸ that was used to find F1. Determine crossingpoint O where  segment F-G crosses the side of M1. Determine the midtpoint N of F-O and draw a circle with radius N-O. Copy that circle to A.

As you can see this circle is virtually 0,5 F-G, but the vesica pisces that determines N does in fact not touches G. There is a tiny discrepance. When drawing by hand it is of no concern unless you use a nano tipped laser guided pencil. Or if you use a vector programe, use O.

This basicly completes the construction fase. All the triangles are now determined. They just have to be drawn. Make a vesica pisces to construct a equilateral triangle P-Q-R in the central circle and extend the sides upward. This will be F3 later on.

Construct triangle J-P-Q and extend downward to determine M3.

By making the central triangle equilateral we can assure that every geometric centrepoint is at the same place and positioned at the centre of the big circle (credit to Sri Yantra research for that one).

So in order to construct the whole diagram only three aspects have to be determined. After that every other aspect is related to this. Everything is connected.

Not only are we through with construction lines, from here we are allso through with accurate proportions. In order to make a Sri yantra that is correctly drawn we have to let go of shapes how we want them to be. For example F2 and M2 can be constructed using the crossingpoints that are in place. They seem equilateral, and maybe they ought to be, but this is not the case. The base angle of F2 is 60,7°. The base angle of M2 is 60,8°.

After M2 and F2 it is possible to complete F3 and M3. The remaining triangles can be drawn in the following order M4, F4 and F5. Again M3, F4 and M4 seem to share the same angles, but this is not the case. But the most important Near Miss is the relationship between F1 and F5. As you can see, they seem to be the same. Not only the same angles, but allso the relative position of the Bintu looks equal. This brings in another aspect that feels right in a cosmogenic diagram; The proces started with F1 and ends with a triangle that is the same. It has a fractall quallity, an infinite series of ever manifestating triangles.

If only this was true. The angles are not the same. Respectivly 36° and 35,7°. Nevertheless, i think the diagram can be contemplated on as such, as long as we don't mention the hard numbers.

The error that is unavoidable is at crossingpoint R.

Remember that the big circle A-B had a radius of 100. The error can be contained in a circle with a radius of 0,00063. In other words; if this Sri Yantra was drawn with a radius of 1 mtr, the error would have a radius of 6 µm That is small enough to contain a single bacterium!

Everything is relative. I chose to give meaning to the ɸ proportions and the equilateral central triangle. Other constructions may prefer to lett F2 and M2 equilateral. I would like to find a construction that emphasises the relationship between F1 and F5. I don't believe one is more right or wrong than the other (from a geometrical vieuwpoint). (But i do am very happy with a 0,00063 error. Doubt if i ever can beat that).

Traditional constructions (for as far as they are known), don't seem to give so much meaning to geometrical accuracy. I would not dream to suggest that Indian culture just wasn't advanced enough to come up with a more accurate construction. There is the callendar function, there is the right intention with which every line has to be drawn, there is a 5000 year gap. The wise man shakes his head, while i get wind up about my 0,00063 error.

The most comprehensive work on the Sri Yantra that is availale on the internet may not be the one that is on top of a Google search; please visit:

https://issuu.com/aumsiva/docs/quest_for_the_sacred_sri_chakram_the_geometric_due

thank you for reading-