Monday, 27 May 2013

Pythogorean theorem in Chamakam

While doing Rudrabhishekam to Lord Shiva, My father explained geometry involved in Mantras of Chamakam. 

Srirudram, is a hymn devoted to lord Shiva. It is part of the Yajur Veda. Sri Rudram is in two parts. The first part, chapter 16 of the Yajurveda, is known as Namakam because of the repeated use of the word "Namo" in it. The second part, chapter18 of the Yajurveda, is known as chamakam because of the repeated use of the words"Chame".Rudram is divided into 11 sections called Anuvakas.

The tenth Anuvaka of Chamakam consists of the following Manthras. 

The Manthra is in Sanskrit is as follows:

Ekaa cha me tisrashcha me pajncha cha me sapta cha me nava cha ma ekadasha cha metrayodasha cha me pamchadasha cha me saptadasha cha menavadasha cha ma eka vishatishcha me trayovishatishcha mepamchavishatishcha me saptavishatishcha me navavishatishcha maekatrishachcha me trayastrishachcha me chatasrashcha meashhtau cha me dvaadasha cha me shhodasha cha me vishatishcha me chaturvishatishcha me ashhtaavishatishcha me vaatrishachcha me shhattrishachcha me chatvarishachcha mechatushchatvaarishachcha meashhtaachatvaarishachcha mevaajashcha prasavashchaapijashcha kratushcha suvashcha muurdhaa chavyashniyashcha antyaayanashcha antyashcha bhauvanashchabhuvanashchaadhipatishcha

Meaning of the above Manthra ( Following meaning may be exact, but inner meaning can be different. Scholars are capable of providing the real meaning of it )  :

Let me be granted the numbers  one, three, five, seven, Nine, eleven, thirteen, fifteen, seventeen, Nineteen, twenty one, twenty three, twenty five, twenty seven, twenty Nine, thirty one, and thirty three, and numbers four, eight, twelve, and sixteen, twenty, twentyfour, twenty eight, thirty two thirty six, and forty forty four, and forty eight to ensure food and its production, its continuity, and the urge to enjoy, the origin of all productions, the sun, the heaven, the head of all, the infinite, the all pervading like the sky, time and the like present at the end of total consummation exists at the end of it on the earth as universal form, the Antaryami the immortal, the inner ruler of every thing, the omni present and omni potent. 

As explained above, the numbers observed initially are uneven numbers 1,3,5,7,9,11,13,15,17,19,21,23,25, 27,29,31, and 33. All these numbers are colored in "RED" in the above diagram.The entire square is divided in to 16 small squares and 64 triangles. If the entire square is folded in the Middle, both sides are symmetric; that is the place where the number 33 crossed the Middle of the square.  Each small square is symmetric with crossed lines forming triangles.

Even Numbers are 4,8,12,16,20,24,28,32,36,40,44,and 48. Each number explains the number of cumulative triangles in each square.

If we observe the above diagram, Middle of the square points are connected and another square is formed. The area of the new square (32 Triangles) is exactly half of the area of the square of the original square (64 Triangles). This can be continued and the shape is formed as follows: 

This is the construction methodology that is followed as the roof of the Garbhalayam above the main deity inside every Hindu Temple.

Pythogorean theorem

Consider the hypotenuse of any triangle, area of the square of it is equal to area of the square of the two sides. As explained in

Even Pythogorean theorem is explained internally in the Hymn. Pictorial description is as follows:

References: Rudhradhyayam