Showing posts with label India. Show all posts
Showing posts with label India. Show all posts

Thursday, May 19, 2016

Sanskrit Shlokas on Mothers Day

Here are few lovely Sanskrit shloka on MOTHER to share with you on Mother's Day! This will help us realize how we treated or expected to be treated 'mother' and 'women' in our society during ancient days.

1. आयु: पुमान् यश: स्वर्ग कीर्ति पुण्यं बलं श्रियं ।
    पशु सुखं धनं धान्यं प्राप्नुयान्मातृ वन्दनात् ।।


A man who serve mother truthfully will be blessed with long life, success, haven, fame, Laxmi, wealth, cattle, food grain, and everything.



2. जननि जन्मभूमिश्च स्वर्गादपि गरीयसि 

After Ravana's defeat, lord Rama said to Laxman, "Own Mother and birthplace are beautiful and greater than haven."
When Laxman, younger brother of Rama asked Lord Rama to acquire the kingdom (Sri-Lanka) after they had defeated and killed Ravana in the war, Lord Rama advised him to hand over the kingdom to Bibhishan, Ravana's younger brother, a rightful king as it was his mother land and Bibhishan inherited it after his elder brother's death. We must respect others' land or wealth (or women) without thinking of acquiring it in anyway. 

3. मातृपितृकृताभ्यासो गुणितामेति बालकः । 
    न गर्भच्युतिमात्रेण पुत्रो भवति पण्डितः ।।

Indian mother and father insist on studies so that their child gain adequate knowledge and skill to lead a respectable life. There is a saying - a king is respected within his kingdom, but a knowledgeable person is respected everywhere.

4. मातृवत परदारेषु परद्रव्येषु लोष्टवत्। आत्मवत् सर्वभूतेषु यः पश्यति स पंडितः।। 

A noble people treat and respect all the women (except his own wife) as mothers. They consider others' wealth as dust and have no intention of acquiring it in anyway. In addition, they also treat and love every living-being or creature and cause no harm to them in anyway.

5. माता मित्रं पिता चेति स्वभावात् त्रतयं हितम् |
    कार्यकारणतश्चान्ये भवन्ति हितबुद्धय: ||

Mother, father and friends are the only people who are interested in your well-being in real way. Thinking of 'good' about you is part of their nature and they do it without any condition or expectation or personal gain. So, value them as others in your life may have business/professional relationship based on certain spoken or unspoken terms and condition/benefits.

6. आदौ माता गुरौ पत्नी ब्राह्मणी राजपत्निका
    धेनुर्धात्री तथा प्रथ्वी सप्तैता मातरः स्मृतः

The ancient Indian tradition teaches us to respect our own mother first, then others in following order - teacher's wife (a brahmin lady), a queen, a cow, a foster mother and the mother earth.  We consider them as MOTHER and respect them at par...


7. मातृदेवीम नमस्तुभ्यं मम जन्मदात्रिम त्वम् नमो नमः ।
    बाल्यकाले मां पालन कृत्वा मातृकाभ्यो त्वम् नमाम्यहम ॥

I salute my mother who gave me birth; I also salute my other mothers (women) who added knowledge and wisdom to my actions and life to make me a good human being.

8. मातृ देवो भव् पितृ देवो भव्
    आचार्य देवो भव्, अतिथि देवो भव्

Let you be one who worships mother, father, teachers and guests as 'God'.

When we study our ancient scripture, we realize that there is profound respect given to mother and women in general. So, read the original scripture to know yourself.

Mother's Day

Tuesday, May 3, 2016

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

Tuesday, March 8, 2016

Respecting Women is an old Indian tradition...

Respecting women is always been part of our culture since it's origin...
यत्र नार्यस्तु पूज्यन्ते रमन्ते तत्र देवताः ।
यत्रैतास्तु न पूज्यन्ते सर्वास्तत्राफलाः क्रियाः ॥
he divine are extremely happy where women are respected ;
where they are not, all actions (projects) are fruitless.
या श्री: स्वयं सुकृतिनां भवनेषु
Who is the Goddess of Fortune Herself in the families of the meritorious
अलक्ष्मीः पापात्मनां
The Goddess of ill luck in the homes of the sinful
त्वं श्रीस्त्वमीश्वरी त्वं ह्रीः
Thou art the Goddess of Fortune, Thou art the supreme Goddess, Thou art Modesty
या देवी सर्वभूतेषु शक्तिरूपेण संस्थिता
The Goddess who resides in all beings as Power
त्वं स्त्रि त्बं पुमानसि त्वं कुमार उत वा कुमारी
Thou art the woman, Thou art the man, Thou art the boy and the girl as well.
Source: Internet

#Ancient #Hindu #Knowledge #customs #Hindu #Hinduism #India #lifestyle #culture #women #respect #international #women #day

Wednesday, December 9, 2015

Aryabhat and his work in Mathematics

Most of us know the invention of zero ‘0’ by Aryabhat in India; but very few know about him or his real work in detail. Aryabhat was a famous Indian mathematician and an astronomer who lived between 476 – 550 CE. Most of his work was done towards end of 4th century CE.
He received his early education in Kusumpura, which is now known as Patna in Bihar.
He had done enormous work in mathematics and astronomy that is complied into two major works and few notes. One of the major works is known as “Aryabhatiya” that has survived the passage of time. 

However, his other work in astronomical computation that is known, as ‘Arya-siddhanta’ could not survive.
Aryabhatiya mainly focuses on mathematics and astronomy and it consists of 4 parts:
1. The Dasagitika Sutra: It has 33 verses that defines the basics of astronomical tables
2. Ganita – Mathematics: This section has 33 verses that give 66 mathematical rules.
3. Kalakriya – The measure of time: This section has 25 verses that describe time, its measurement and planetary models.
4. Gola – The spherics: This section has 50 verses those details on sphere and eclipses.
Here is the extract of some of his work for us to gauge the depth of knowledge that India lost over a period of time.

i. Most basic & famous example of binomial:

(a + b) ² = a² + 2ab + b²
Or
a X b = (a+b)2  - (a2 – b2)
------------------------
2

ii. Value of Pi:


abhi svav Rushtim madey ays yudhyato raghveeriva pravaNe samsrutaya: | indro yad vajree dhRuSHamANo andhasA behind valasya paridheemriva trita: ||
paridhi m. circumference Paridhih +iva+ tritah. Paridhih means circumference, iva means like or for example, tritah means by 3. Thus, like circumference by three.



haturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇāmayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.
"
Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."

This implies that the ratio of the circumference to the diameter is:
((4 + 100) × 8 + 62000)/20000
= 62832/20000
= 3.14159265 i.e. the value of π is correct to 8 places

iii. The value of pie upto
गोपीभाग्य मधुव्रातः श्रुंगशोदधि संधिगः |
खलजीवितखाताव गलहाला रसंधरः ||
gopeebhaagya maDhuvraathaH shruMgashodhaDhi saMDhigaH
khalajeevithakhaathaava galahaalaa rasaMDharaH
ga-3, pa-1, bha-4, ya -1, ma-5, Dhu-9, ra-2, tha-6, shru-5, ga-3, sho-5, dha-8, Dhi -9, sa-7, Dha- 9, ga-3, kha-2, la-3, jee-8, vi-4, tha-6, kha-2, tha-6, va-4, ga-3, la-3, ha-8, la-3, ra-2, sa-7, Dha-9, ra-2
π  = 3.1415926535897932384626433832792...

iv. Measurement of earth:
About the circumference of the earth, Aryabhat measured as 4 967 yojanas (1 yojana = 5 miles) and its diameter as 1 5811/24 yojanas.
5 x 1 5811/24
= 24835
And, today it is measured as 24 902 miles (using all the advanced equipment, technologies)
Sine differences: The rules says each sine-difference reduced by quotients of all the previous differences and itself by the first difference.
d2 (sin x)
--------------   = - Sin x
dx2
For example, check the numbers - 51, 37, 22, 7

v. Earth and planetary light:
Aryabhat has mentioned that the Moon and planets shine by reflected sunlight.
vi. Rotation of earth:
In his golapada stanza 9, he wrote:


He also mentioned the unconventional discovery about the rotation of the heavens was due to the axial rotation of the Earth on daily basis; that apparently was accepted much later by the West.
Acknowledging Aryabhat’s contribution in mathematics and astronomy, India honored him by naming its first satellite as ‘Aryabhat.’
If the Indian government takes interest in teaching ancient languages and investing into ancient scientific scriptures, it can build stronger scientific base in future. Apparently, it was believed that Germans learned Sanskrit to rediscover Indian scientific and technological advancement in aeronautical field and they succeeded in building an advanced plane. That knowledge was eventually taken by NASA scientists after World War II and used in their research.
Image Credits: Wikimedia Commons
References:
  • J. J. O'Connor and E. F. Robertson, Aryabhata the Elder, MacTutor History of Mathematics archive
  • http://www.ms.uky.edu/~sohum/AAK/pdf%20files/aryabhatta.pdf_
  • Understanding (Third Edition). New York: W.H. Freeman and Company. p. 70. ISBN 0-7167-4361-2
  • https://en.wikipedia.org/wiki/Aryabhata
  • http://www-history.mcs.st-and.ac.uk/Biographies/Aryabhata_I.html