My wife and I are planning a big trip to India early next year. When I think of India and geometry, two things immediately come to mind: the Taj Mahal, and the Sri Yantra. Everyone knows what the Taj Mahal is, but have you heard of the Sri Yantra?

## What is the Sri Yantra?

You have probably seen a Sri Yantra even if you haven’t heard the name for it. It looks like this:

And is often surrounded by additional ornamentation representing lotus petals, etc. like this:

This symbol (both the basic form and the full ornamented form above) is laden with many layers of meaning in Hindu philosophy, which you can read about in the Wikipedia article on Sri Yantra. However, I’m going to focus on the geometry, as you might expect.

### An Acknowledgement

Before I dive in I want to note that much of what I am presenting (including a number of the images) I found a wonderful site called **Sri Yantra Geometry Research** (www.sriyantraresearch.com). If you enjoy this post, you ** must** go to this site, where you can spend hours (as I did!) learning all the finer details about this amazing figure.

## Sri Yantra Basic Definitions

So, what make a Sri Yantra a Sri Yantra? In short, it is a figure composed of nine triangles and a central point (called the *bindhi*) such that:

- Four triangles point up and five point down
- The corners of the two biggest triangles all touch the same outer circle
- For all the other triangles, the uppermost or lowermost point touches the base of an opposite-pointing triangle
- At
*eighteen*different points, three triangles cross at a mutual point! - The central bindhi is located at the geometric center of the innermost triangle (formed by the crossing of two of the downward-pointing triangles)

So, which one is the “right one”??

## The “Optimal” Sri Yantra

It turns out that an optimal figure has three important properties:

### Concurrency = Everything Touches/Intersects Perfectly

**concurrency**, which is simply the property described above where all the triangles touch and intersect with each other perfectly at their meeting points. It turns out that there are a LOT of figures out there that are “fudged” – in other words, where three triangles

*seem*to meet in a point but they actually miss each other slightly:

### Concentricity = Centers Match

**concentricity**, which means “shared center.” In this case, what we mean is that the bindhi should land in the same place as the center of the large surrounding circle. Here is an example of a concentricity error (the green lines show the center of the surrounding circle which is outside of this diagram):

### Equilaterality = Center Triangle Has Equal Sides

**equilateral**, meaning all three sides will have the same length and all three angles will be 60 degrees. Very often this is not the case:

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