The Constructions and these tables imply a great knowledge of geometry,arithmetic and even of the theoretical part of astronomy.But what, without doubt is to be accounted,the greatest refinement in this system, is the hypothesis employed in calculating the equation of the centre for the Sun,Moon and the planets that of a circular orbit having a double eccentricity or having its centre in the middle between the earth and the point about which the angular motion is uniform.If to this we add the great extent of the geometrical knowledge required to combine this and the other principles of their astronomy together and to deduce from them the just conclusion;the possession of a calculus equivalent to trigonometry and lastly their approximation to the quadrature of the circle, we shall be astonished at the magnitude of that body of science which must have enlightened the inhabitants of India in some remote age and which whatever it may have communicated to the Western nations appears to have received another from them….”  – John Playfair about Indian Maths

The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. The importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of antiquity, Archimedes and Apollonius. – Laplace about Indian Maths

The a priori theorems of Mathematics are the Ideas of Plato and the Eternal Order of Spinoza !

Mathematica Indica 

Sanskrit poets used  Elemental Numbers in their poems. As eyes are 2, two represents eyes. As the Vedas are four, four represents the Vedas. Netra Netra ( eyes , eyes ) means 22 and Veda Veda means 44. 

Here we give the correspondence between numbers and the Elements


1. Earth, Moon
2. Eyes, hands, feet, ears
3. Worlds, trinitarian unity, three yogas, three vedas.
4. Vedas 
5. Sense organs.
6 Rithus or the six seasons.
7. Rishies
8 Directions, eightfold prosperity
9 Digits, numbers
0 Ether


10 – Ego and its ten heads.
11 – Rudras
12 Months, Zodiacal Signs
13 Universe
14 Vidyas, Manus
15 Lunations, thidhis
16 King
17 Athushti
18 Treatises astronomical, mythological
19 Athi Dhruthi
20 Nails
21 Uthkruthi 
22 Akrithi
23 Vikruthi
24 Gayathri
25 Principles
27 Constellations
33 Deities


The digits for the letters are written, counting from right to left

For example,

Bhanandagni

Bham = Stars = 27
Nandan = 9
Agni = 3

Bhanandagni = 3927
Known as Paral Sankhya, the Alpha Numeric System was developed by Vararuchi. It is also known as Katapayadi, as 1 represents the letters Ka, Ta, Pa and Ya, whose corresponding digit is 1. 


Number Letters

1 ka ta pa ya
2 kha tta pha ra
3 hu da bha la
4 gha da ba va
5 nga na ma sha
6 cha tha sha
7 chha dha sa
8 ja dha ha
9 jha ddha
0 nja na ksha 

The Value of Kaa ki ku ke and ko was 1


31 was represented by Kala 

Kala is ka + la = 31 ( The digits are counted from the right )

and 351 by Kamala
Kamala = ka + ma + la = 351
Ganitha Kerala, the Kerala School of Astronomy and Maths, has given a lot of names for big numbers.

Like the Western 

Myriad = 10^4
Million = 10^6

Indian names are 

Shata = 10^2
Sahasra = 10^3
Ayutha = 10^4
Laksha = 10^5
Dasa Laksha = 10^6 ( Million ) 
Koti = 10^7
Dasa Koti = 10^8
Vrinda = 10^9
Kharva = 10^10
Nikharva = 10^11
Mahapadma = 10^12
Mahakharva = 10^13
Padma = 10^14

In the Western, we have

Million = 1000^2
Billion = 1000^3
Trillion = 1000^4

or 

Nillion = 1000^(n+1)

where n is the number. Tri meaning 3 and trillion = 1000^(3+1)!
There are greater numbers, than the ones mentioned below. 
Maha Padma = 10^15
Kshoni = 10^16
Parardha = 10^17
Sankha = 10^18
Maha Sankha = 10^19
Kshithi = 10^20
Maha Kshiti = 10^21
Kshobha = 10^22
Maha Kshobha = 10^23

Neethi Lamba = 10^27
Sarva Bala = 10^45
Thallakshana = 10^83
“By one more than the one before” – A sutra of Vedic Maths

Ekadhikena Purvecha is Sanskrit for ” One more than the previous one”. This 
sutra can be used for multiplying or dividing algorithms.

You can use this formula to compute the squares of numbers.

For example.

35×35 = ((3×3)+3),25 = 12,25 and 125×125 = ((12×12)+12),25 = 156,25

By the sūtra, multiply “by one more than the previous one.”

35×35 = ((3×4),25 = 12,25 and 125×125 = ((12×13),25 = 156,25

 


Happy Makara Pathu is advance. Tomorrow, 24 0118. Celebrations at Narayamkulangara Devi Temple, Guruvayur.

https://www.youtube.com/embed/vSv2MvPnPWI

Pathue means Ten in Malayalam. Patham Udayam is the Tenth Rising of the Sun in Aries, Meda Pathu, when Sun’s longitude touches 10 degrees..

Longitude of Sun                                   Event
10 degreesMeda Pathu, Patham Udayam
40Edava Pathu
70Mithuna Pathu
100Karkitaka Pathu
130Chinga Pathu
160Kanni Pathu
190Thula Pathu
220Vrischika Pathu
250Dhanu Pathu, farmers start watering
280Makara Pathu
310Kumbha Pathu
340Meena Pathu

In Indian Philosophy, no Hegelian obfuscation, no Pythagorean adumbration, no Marxian double talk, exist !

The Mathematical, Absolute Brahman


Any number into Infinity is Infinity,
Any number into Zero is Zero
Then what is Zero into Infinity?
Mathematically, an Indeterminate.

Brahman has been defined as Infinity (Anantam Brahma )
And also as Zero ( Shoonyam ennum chilar )
So, what is He really?
Philosophically, an Indeterminate.


Ganitha Sastra is the Science of magnitude,
The Science of the more or less,
The Science of quantities,
But, is the Science of the Infinite !

Universe has neither Center nor Circumference.
It would have had a Center, if Circumference existed.
Since it cannot be enclosed within any Center or Circumference
It would be unintelligible, without the Absolute , being both.

The Absolute is an Infinite Sphere,
Center everywhere, Circumference nowhere.
This is the second best Definition,
The first being Being-Knowledge-Bliss !


At Infinity, Center and Circumference are one,
Maxima and minima coincide.
Science and Art meet at Infinity,
Past, Present and Future become one.

Maths became Meta Maths,
When Godel declared that Truth,
Cannot be represented by finitude,
As it is non finite and transcendental !