Brahmagupta’s contribution to Mathematics - Rules for "zero"

Against the popular perception, I would say that none including Aryabhat has invented ‘zero’ because the concept of ‘zero’ was always part of our life in different way academically or professionally since the origin of the universe.

Brahagupata’s major contribution to modern science and technology was - how to use zero in mathematical calculations that is used as base to calculate every field. He has formed the set of rules in the mathematics for positive and negative number in addition to forming the rules for using zeros in calculations and that has become the basis of mathematics and rest of the field including economics, finance, physics, chemistry, astronomy and so on…

Brahmagupta was born in 598 CE and died in c. 670. He lived in during king Vyagrahamukha in Bhillamala (modern Bhinmal) a capital of Gurjaradesa Chapa dynasty, one of the largesst kingdoms of Western India in parts of southern Rajasthan and Northern Gujarat.

He studied 5 traditional siddhantas in Brahmapaska in one of top schools for the astronomy during those days.

He also studied his predecessors’ (Aryabhata I, Latadeva, Pradyumna, Varahamihira, Simha, Srisena, Vijayanandin and Vishnuchandra) work to continue their research work. His rules of zero is in continuation of Aryabhata I ‘s work.

Brahmagupta gave the solution of the general linear in chapter eighteen of Brahmasphutasiddhanta,

bx + c = dx + e equivalent to x =< (e−c) / (b-d)


In chapter eighteen of Brahmasphutasiddhanta, Brahmagupta describes operations on negative numbers. He first describes addition and subtraction,

18.30 (Additions)

· 3 + 4 = 7 (a positive number)

· -3 + (-4) = -7 (a negative number)

· -3 + 4 = 1 (positive number)

· 3 + (-4) = -1 (negative number)

· -3 + 3 = 0 (zero when both positive and negative numbers are same)

· -3 + 0 = -3 (negative number)

· 3 + 0 = 3 (positive number)

· 0 + 0 = 0 (no difference)

18.32 (subtractions)

· -3 – 0 = -3 (negative number)

· 3 – 0 = 3 (positive number)

· 0 - 0 = 0 (no difference)

· 3 - (-4) = -1 (negative number is added)

· -3 – 4 = - 7 (negative number is added)

18.33(Multiplication)

· 3 * - 4 = - 12 (one negative and one positive product becomes negative number)

· 3 * - 4 = 12 (two negative becomes positive)

· 3 * 0 = 0 (any number multiplied with zero is zero)

18.34 (Division)

·     3
     ----  = 1 (positive number)
      3

·    - 3
       ----  = 1 (positive number)
      -3

·    0
    ---  = 0 (zero)
     0

·     3
     --- = -1
     -3

·      -3
      ---  = -1
       3

·    √0   =  0

·    0 square   = 0

·    0
    ----
     0

·    3
    ---- = undefined
     0

Except the last definition of zero, we use all his rules in the modern mathematics.

Watch out this space for part II on his other contributions in calculating complex mathematical formulas.

References:

Brahmagupta (598–668)," Department of Mathematics, Simon Fraser University (British Columbia, Canada), http;//www.math.sfu.ca/histmath/India/7thCenturyAD/Brahmagupta.html (February 17, 2006).

"Brahmagupta (ca. 598–ca. 665)," Wolfram Research, http://www.scienceworld.wolfram.com/biography/Brahmagupta.html (February 17, 2006).

"Brahmagupta," School of Mathematics and Statistics, St. Andrews University, http://www-groups.dcs.st-and.ac.uk/∼history/Mathematicians/Brahmagupta.html (February 17, 2006).

"Brahmagupta," Vidyapatha, http://www.vidyapatha.com/scientists/brahmagupta.php (February 17, 2006).

http://www.encyclopedia.com/topic/Brahmagupta.aspx

अहिंसा (Non-violence) a misunderstood term in Hinduism

अहिंसा परमो धर्म; धर्म हिंसा तथीव च |

अर्थात
अहिंसा मनुष्य का परम धर्म है और धर्म की रक्षा के
लिए हिंसा करना उस से भी श्रेष्ठ है...!!!!

Mahatma Gandhi popularized only part of the Gita quote and I mentioned about this in oct 2014 on Facebook. he perched and popularised partial quote and misguided the nation in the freedom struggle.

Non-violence is the ultimate dharma. But, violence is essential to protect people, their land and the nation and this is every King’s duty (धर्म) that he needs to follow...

1.Rama didn't forgive Ravana in-spite of Ravana being one of the most revered and respected kings at that time having greatest knowledge in Music, Architecture and warfare. His act of abducting other's wife (अबला) who was alone and couldn't defend herself, was just unforgivable and Rama mentioned that they didn't want to set this as an acceptable trend. 

2. Krishna advised Arjuna that the act of Drupadi ‘vastraharan’ (disrobing) was not acceptable in anyway. The reason he mentioned was Drupadi was a daughter of powerful king, gifted woman herself, a wife of noble men and a future queen.

He further said, "If you forgive Duryodhan for humiliating such a powerful and respectable woman, there will be no respect for common women in the society." 

3. Prithvi Raj Chauhan, a famous Rajput King forgave Md Ghori 16 times as mentioned by few historians. However, when Md Ghori got an opportunity to defeat the Rajput king deceitfully (as his confidant officer, Jaichand helped Md Ghori to capture the king), he did NOT reciprocate the act of 'forgiveness' for once. On the contrary, he killed the Rajput king by torturing him as inhumanly as possible. History witnessed this.

Hinduism talks about compassion(माया), kindness(करूणा) and harmony(सहचार) with every living being, not just restricted to human being. Therefore, there are festivals where Hindus worship cow, bulls, elephants, and the snakes (during nagpanchami). This peace and kindness is also extended to mother nature to value their contribution in our life. The Hindus also revere Mother Nature such as river, the mountain, the farm, the produce and the soil.

So, forgiveness is depends on the situations and thus, non-violence is a relative terms and must be used cautiously.

#compassion #customs #gandhi #Hindu #kindness #love #misunderstood #nonviolence #practices #religion #Sanatana Dharma #violence VedicGyaan #vedicknowledge #sandhyajane