Prof. Muni Mahendra Kumar
There is a cylindrical pit measuring one yojana each in length, breadth and height based on utsedha aṅgula. It is made cram-full with the billions of hair-tips of humans of Devakuru-Uttarakuru region. Before calculating the number of hair-tips, filled in pit, we have to calculate the volume of the cylinder. The base of the cylinder is circular. Area of circular base = πr2 (where r is radius).
Volume of the cylindrical pit = = πr2h (where h is height).
In this equation, the value[1] of π, taken into account, is - 19/6.
According to the table of space-units
1 yojana = 7,68,000 utsedha-aṅgulas.
There are 87 hair-tips of humans of Devakuru-Uttarakuru region in one utsedha-aṅgula space. Therefore,
1 yojana = 87 x 7,68,000 hair-tips of Devakuru-Uttarakuru humans.[2]
[Since the diameter (further denoted as d) is one yojana.]
d = 87 x 7,68,000
∴ r = d/2 = (87 x 7,68,000)/2
[h is equivalent to d over here. So]
h = 87 x 7,68,000
∴ Volume of the cylindrical pit = πr2h
= 19/6 x (87 x 7,68,000)3 /4
= 330,762,104,246,562,542,199,609,753,600,000,000,0
= 3.3 x 1036 approximately.[3]
So, the number of hair-tips of Devakuru-Uttarakuru humans filled in the cylindrical pit is 3.3 x 1036.
The hair-tips are taken out of it in four ways.[4] On the basis of these different ways, Palyopamas are of four types
Circumference divided by diameter of a circle is equal to π. Attempts have been made from ancient time to evaluate its numerical value. In Jain canonical literature, 'more than three' these words are used for π (see Aṇuogadārāiṃ, the topic of upamā, sūtra 422). In post-canonical Jain literature, the value given is 19/6 or √10 (see Trilokasāra, verse 17; Tiloyapaṇṇatti, 1-117; Lokaprakāśa, 1-7). Also in non-Jain ancient scriptures, the value of π is √10 (see Prācīna Bhārata men Gaṇita kā Yoga, p. 8). According to one verse of
ṣaṭkhaṇḍāgama's Ṭīkā named Dhavalā by Vīrasenācārya, the value of π is (3 + +) (where d is diameter). See ṣaṭkhaṇḍāgama, in 1-3-2, verse 14, book 4, p. 42. In this verse, the value of the first term comes to be 3.14159292..... According to modern mathematics, value of π is expressed in following
progressive series: π = 4 (1-1/3+1/5-1/7+1/9-1/11+...........)
Calculating its value to 14 decimal places, we get π = 3.1415926538979.
(See Geometry, by Charles M. Bloomfield, Robert Icolf and Maril E.Shanks, pp. 204, 205.
