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

Why Hindus Worship 'Shiva Linga'?

The lingam or Shiva Linga is the most sacred symbol of Hinduism, as it represents the Lord Shiva, who is worshiped across the Indian subcontinent by Hindus.

Contrary to popular belief that originates from partial meaning of Linga, there is an altogether different meaning and significance to Shiva Linga that is far beyond this superficial belief.

The Meaning of Shiva Linga.

Shiv Linga symbolizes the God himself or his source of energy or cosmic eggs (Brahmanada), and signifies emergence or origin. The base of Shiv Linga represents female yoni, which signifies mergence; thus, Shiv Linga forms highest source of energy in the universe where every life begins...this is the symbol of emerging or beginning of life and merging into the momentary life where everything is ephemeral. The true identity of Shiva Linga is shoonya – void – and symbolizes the sign of zero in ancient mathematics. This also conveys the teaching of leading an “egoless” life in the service of people and the god. The Ganga on the Shiva's head represent the river meeting ocean i.e. devote 'self' into god/universe.

Hindus have always considered life in totality and connect it with universe. The body and energy points, or Chakra, are all scientifically explained and well connected with culture through various religious and cultural practices.

“Self” is not given importance and thus, the Western concept of describing Shiva Linga is factually incorrect.

Shiva Linga and it's concept

The Mythological Story.

The popular and powerful sage Shukaracharya was visiting Lord Shiva in Kailash, one of the sacred Hindu mountains in the Himalayas. When he reached Kailash, he saw that Lord Shiva was busy copulating with Shakti (Goddess Parvathy, Lord Shiva's wife). Lord Shiva was so engrossed in the act that he didn't realize the presence of Sage Shukaracharya. The Sage, well known for his short temper, got annoyed and cursed Lord Shiva in that people would worship his Linga (genitalia) in the future, which was against the usual worshiping practices/norms.

Mahashivaratri.

"Nature specializes in a kind of paradox: Nature destroys and her destruction is always constructive destruction. The bud is destroyed when the flower blooms, and the flower fades when the fruit emerges. The fruit decays when seeds are scattered and seeds decay when plants sprout.

“This process of constructive destruction is Shiva, the annihilator. This Shiva-Ratri is the destruction of the ego  in the discovery of the Self (Shiva).“May all devotees come to experience at least the shy rays of the early dawn at the end of one's inner Ratri, in the emerging beams of Shiva’s spirit in us.

“Be quiet. Be silent within. Blind, Deaf, Mum - be. Invoke . Be expectant. Let Shiva happen - TRY." -Swami Chinmayananda

Shiv Temples.

It is also believed that if a person died where people worshiped Shiv Linga, his soul would go to Shiv-Lok or Shiva's world. This is one reason, one will see a “shiva” temple in every part of India from Kailash, the northern point in Himalaya, to Rameshwara, the southern part, and also Somnath in the west to the eastern point of India.

There are twelve main Jyotirlings and five panch-bhuta Lingas in India.

The 12 Jyotir-Lingas are as listed below:

1. Kedarnath,

2. Kashi Vishwanath,

3. Somnath,

4. Baijnath,

5. Ghrusneswar,

6. Tryambakeshwar,

7. Bhimshankar,

8. Mahakal,

9. Mallikarjun,

10. Amaleshwar,

11. Nageshwar, and

12. Rameswar

The 5 Pancha-Bhuta Lingas are as below:

1. Kalahastishwar,

2. Jambukeshwar,

3. Arunachaleshwar,

4. Ekambareshwar of Kanjivaram, and

5. Nataraja of Chidambaram.

सत्य ही शिव है । शिव ही सुन्दर हैं ।

#Mahashivratri #shiva #shiv lingam #linga #hindu #Hinduism #mythology #zero #devotion #spirituality #sandhyajane