Size and Shape of Yagya Kund: Mathematical and Spiritual aspects

The size and shape of the Yagya Kund is one of the important aspects for successful completion of Yagya. Vedic literature describes in details about their types, size, shapes and constructions. Yagya Kund size and shape helps in construction of the Kund for specific spiritual or materialistic outcomes which require specific mathematical measurements of Yagya Kund. The shape of the Yagya Kund is decided based on the purpose of the Yagya, while the size is decided based on the total offerings given to the fire. The spiritual and mathematical aspects on size and shape of the Kund are presented in the study. During the study analysis, it was observed that Vedic texts used mathematical knowledge from various streams such as astrology, trigonometry, geometry, etc in the construction of Yagya Kund. The size of Yagya Kund is directly propositional to the number of offerings to be done. In addition, during the construction of any Yagya Kund, first of all a circle is made whose parameter is fixed to the number of offerings to be done, then a particular Yagya Kund is to be constructed. Regardless of the shape, the construction of Kund based on the diameter given in the ancient texts resulted in the same surface area and volume for particular number of offerings, opening a gate for further study of fine mathematics involved in the Yagya Kund construction.


Introduction
Yagya is an essential part of Indian culture. According to Indian scripture, the human life runs on the philosophy of Yagya from birth to the end. In Indian culture conceiving (garbhdhan) is also a kind of Yagya and so the funeral (anteyeshti). There are three root meanings of word Yagya i.e. to worship (dev poojan), to harmonize (sangatikaran) and to bestow (daan) (1,2). Yagya is being used for different purposes for spiritual or materialistic desire and One of the central aspect in this regard is shape and size of the Fire pit. The Vedic ritual Yagya is done in the fire pot termed as Kund.
As per the Panini Grammar the root (dhatu) of the word Kund implies for meanings -1) protective place (rakshanarthkudi), 2) object of the measurement (manarthkkun), 3) the opening place, nurturer, place of fire, pot for water (koshkaar Kund), etc. Here for the perspective of Yagya, it is taken as the place for fire of Hawan (Yagya). Thus, Vedic literature describes Kund as a medium to offer havi (offerings) to divine and the whole process as Yagya (2). This Vedic ritual Yagya includes very strict mathematical measurement for every part of the ritual. The size of Mandap is dependent on the size of the Kund and the size of the Kund is dependent on the number of offerings. The number of offerings is dependent on the spiritual penance (Dharm-anushthan) it was meant for.
In Vedic times the science of Yagya has highly evolved. This is reflected in different types of materials and tools used in the Yagya with detailed protocols of their construction and utility. One such aspect of Yagya is the size and shapes of Yagya Kund.
The size and shape of the Yagya Kund is one of the important aspects for successful completion of Yagya. Vedic literature describes in details about their types, size, shapes and constructions. Yagya Kund size and shape helps in construction of the Kund for specific spiritual or materialistic outcomes which require specific mathematical measurements of Yagya Kund.
The spiritual and mathematical aspects on size and shape of the Kund are presented in the study.

Different shapes of Yagya Kund and their purposes
'Bhavishya Purana' and 'Kund Mandap Siddhi', both books described total 10 types of shapes i.e. Circular, Semi-circular, Vulvar shape, Trigonal shape, Lotus shaped, square shaped, Pentagonal shaped, Hexagonal shaped, Heptagonal shaped and Octagonal shaped. They are shown in Table  1. Different shapes are recommended for specific spiritual and material purposes and ignorance of it, as per the scriptures, it can lead to nullification or reduction of the desired outcome. Table 1 also described their purpose (3,4).
These are the commonly mentioned Yagya Kund shapes. However, there are texts mentioning other types of shapes such as starshaped Hexagonal (vishamshadastra) and starshaped octagonal, etc (vishamashtashtra), etc (2) (Figure 1).  Here 'hand' is used as unit which is not as length but it rather represents area or volume and it is a unit required for construction of the Yagya Kund. The details are as follows. The research article by Shailajkumarshrivastava (5) described 1 Angul as 2.0 cm. The book by Munger Yoga Publications (6) described 1 Angul as 1.9 cm. It also mentioned that the Angul used for calculating the Yagya Kund construction is the measurement of the width of the thumb of the Yajman (host), who is supposed to give the offerings to fire. It also explains that the total volume of offerings is dependent on the size of the finger/Angul of the host. This was the finest calculation used in Yagya Kund construction.

The volume is same of all different shaped YagyaKunds
The most interesting thing in these calculations is that regardless of shape, the volume is kept same for the same amount of offerings as offerings count decides the total volume required ( Table 3).
The diameter of the circle for each type of the Kund shape was previously described in the book 'Kund Mandap Siddhi' (4,8). Also the Vedic formula to calculate the area using diameter (see sloka 13 reference 8) is also described in the book and it was applied as shown in table 3. As it is seen the all 10 shaped with different diameter resulted in same area i.e. 576 Angul which is decided based on the number of offerings as shown in Table 2. Sr. no.

Conclusion
Design and construction of yagya Kund requires very scientific and rigorous mathematical knowledge. Indian sage had developed the science of Yagya Kund construction with very fine mathematical models and they were great scientists. They provided Vedic mathematical formulation for preparation of yagya Kund which is true in current time period too. Regardless of the shapes the total volume& surface area remained same. The different shapes of yagya Kund have different aims as their purpose was to produce different energy with help of different Yagya Kund shapes. The energy science and protocols of different shapes for specific purposes is beyond the scope of this paper but it demands a thorough investigation of this Vedic wisdom.