Sequences of Numbers in Chamakam and their Significance

Sri K Suresh, in a Youtube Video [1], indicated that a particular sequence of numbers in Chamakam interested him.

People, who are not familiar with Chamakam and the numbers, may refer to this Blog [2].

The numbers are: 1, 3, 5, 7, 9, 11, 13, …, 33.

These numbers are not sequential. There appears to be no pattern to them.

Sri Suresh decoded them and found that the sequence of numbers is actually the Differences of Squares of a sequence of Natural Numbers from 1 to 17. That was a good discovery.

But, what do the resulting numbers in Chamakam represent? The numbers could be a coded message of some type. I liked to find out.

I did an Internet search with the keyword Chamakam, which led me to a number of additional references. I am reproducing a few links at the bottom. [3]

The numbers of interest are the sequence of natural numbers, the difference of Squares of successive numbers, and the sum of the successive squares of numbers. Thus, there are three sets of numbers, which would be seen in Figure 1.

Figure 1: Table Showing the Method to Arrive at the Numbers in Chamakam (Source: Screen Clipping from Reference [1]))

The process or method to arrive at these numbers is shown in Figure 2.

Figure 2: The Method to arrive at the Table in Figure 1.

We notice three sequences as follows.

Sequence of Natural Numbers = 0, 1, 2, 3, 4, 5, 6, … 17

Sequence of Squares on Natural Numbers = 0, 1, 4, 9, 16, 25, 36, … 289

Difference of Squares of two successive numbers = -, 1, 3, 5, 7, 9, 11, 13, …, 33

The successive difference between any two numbers = 2

Sum of the Successive Difference of Squares of two successive numbers = -, -, 4, 8, 12, 16, …

Each Sum of the Successive Differences of Squares differs from the prior one by a constant value = 4.

Incidentally, this sequence of numbers is also the sequence of successive natural numbers with each number multiplied by 4, i.e. 4 * (0, 1, 2, 3, 4, …).

While this derivation and arithmetic interpretation is interesting, I wondered what significance these sequences of numbers may have. I checked with friends knowledgeable about texts in Dharma Sastras such as, Sri Rudram and Chamakam if such sequences of numbers were referred in any other context. I will post their responses with their permission when I get them.

As I pondered over this puzzle, the idea of squares of numbers suggested to me areas of surfaces of structures. I wanted to see how a geometric representation would look like. The difference in squares of natural numbers can be represented as the area of a surface formed when two squares intersect as in the plan view of a structure. Thus the series of numbers can be referring to a series of the surface areas as shown in Figure 3. Could the numbers be pointing to a Structure?

Figure 3: The sequences of numbers may represent the areas in the plan of a structure.

That leaves us with the question as to what the other sequence of numbers would represent. The sum value can be the height of each segment as shown in Figure 4.

Figure 4: A Structure that may represent both sequences of Numbers.

Of course, this prompts the question if there is any physical structure specified in the literature with such proportionate dimensions. Of course, that is for the experts to respond.

In the above figures, square shaped bases are shown at each elevation as the discussion dealt with Squares of numbers. However, the base can also be circles as a circle will have an area equal to Pi R ^ 2. Such a structure can look like that shown in Figure 5.

Figure 5: A Structure with Circular Bases.

It occurred to me that since a sphere has a surface area of 4 Pi R ^ 2, the sequence of numbers may represent the difference between the surface areas of successive spheres. But, I could not think of a geometric representation that shows the difference between the surface areas of two spherical segments. Roofs of a structure take such surfaces. I will try later on if it works out.

Sri Panchanana M.R.L.N. presented a geometric explanation for these sequences of numbers in Chamakam. [4]

Another blog, “Mathematics in Chamakam” explains the significance of these sequences of numbers in cultural and religious terms as boons sought by worshippers. [5]

Well! That brings me to the end my ability to think on this topic for now. Hence, I am posting this explanation on the Social Media and am requesting friends to reflect on the question with their knowledge of arithmetic, geometry, and the Dharma Sastras. They can provide a fuller and better explanation.

Now, it is the turn of my friends.

References:

[1] Sri K. Suresh, “Chamakam Decoded | Difference of Squares, My Meeting with Sringeri Swamigal,” Sep 16, 2020 https://www.youtube.com/watch?v=h6ERtEnpcvM

[2] Connect Science To Divinity: Mathematics In Chamakam

[3] Additional Links to Chamakam and Mathematics:

http://isatsang.blogspot.com/2016/07/construction-of-odd-and-even-numbers-in.html

https://vivekitam.wordpress.com/2009/04/28/geb-properties-of-natural-numbers-and-chamakam/

http://connectsciencetodivinity.blogspot.com/2017/04/mathematics-in-chamakam.html

http://satyamparamdheemahi.blogspot.com/2014/01/rudra-chamakam-numbers.html

http://nrsrini.blogspot.com/2012/01/what-do-odd-and-even-numbers-in.html

https://www.astrojyoti.com/srirudram.htm

https://medium.com/@chinmayi.kanugonda/unraveling-the-secrets-of-rudram-athi-rudra-maha-yagya-b4b241ce29f8

https://www.livermoretemple.org/hints/content/html/Maharudram_description.pdf

https://www.starbrightokanagan.ca/forum/chamakam-11th-anuvaka-meaning-88345d

https://www.linkedin.com/pulse/science-essence-sri-rudram-sivkishen-lionlinked-gmail-com/