Tag: Varāhamihira

  • Mathematicians of India Before Christ

    Mathematicians of India Before Christ

    This is in continuation of my earlier article History of Mathematics Preface Bakshali Manuscript.We may now look some ancient Indian treatises on Mathematics.The names that come to one’ s mind are Aryabhatta and Varahamihira.

    Mathematics, Numerals in Brahmi text, India.
    Mathematics in India

    Aryabhatta

    Aryabhata (Sanskrit: आर्यभट, ISO: Āryabhaṭa) or Aryabhata I (476–550 CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta Era and produced works such as the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old) and the Arya-siddhanta.Aryabhata (Sanskrit: आर्यभट, ISO: Āryabhaṭa) or Aryabhata I(476–550 CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta Era and produced works such as the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old) and the Arya-siddhanta.

    His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers , algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.

    The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata’s contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta and Bhaskara.

    Brahmagupta

    Brahmagupta (c. 598 – c. 668 CE) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the Brāhmasphuṭasiddhānta (BSS, “correctly established doctrine of Brahma”, dated 628), a theoretical treatise, and the Khaṇḍakhādyaka (“edible bite”, dated 665), a more practical text.

    • Brāhmasphuṭasiddhānta,composed in 628 CE.
    • Khaṇḍakhādyaka,composed in 665 CE.
    • Grahaṇārkajñāna,(ascribed in one manuscript.

    Lalla

    Lalla (c. 720–790 CE) was an Indian mathematician, astronomer, and astrologer who belonged to a family of astronomers.

    Śiṣyadhīvṛddhidatantra is his work.

    Panini 5th Century BC

    We know Panini to be the grammarian of Sanskrit Language . He was an illustrious Mathematician too. His notation was similar to modern mathematical notation, and used metarules, transformations, and recursion.Pingala (roughly 3rd–1st centuries BC) in his treatise of prosody uses a device corresponding to a binary numeral system. His discussion of the combinatorics of meters corresponds to an elementary version of the binomial theorem. Pingala’s work also contains the basic ideas of Fibonacci numbers. Read this Mathematical Structures of Ashtadyayi

    Pingala 3- 2 Century BC

    Another great mathematician of ancient India.ancient Indian poet and mathematician, the author of the Chandaḥśāstra (also called Pingala-sutras), the earliest known treatise on Metres.( Chandas,Vedic Metres).The Chandaḥśāstra presents the first known description of a binary numeral system in connection with the systematic enumeration of meters with fixed patterns of short and long syllables. The discussion of the combinatorics of meter corresponds to the binomial theorem. Halāyudha’s commentary includes a presentation of Pascal’s triangle (called meruprastāra). Pingala’s work also includes material related to the Fibonacci numbers, called mātrāmeru.

    The Surya Siddhanta,

    Homage to Brahma, Suryasiddhantha

    The Surya Siddhanta ‘The text is known from a 15th-century CE palm-leaf manuscript, and several newer manuscripts. It was composed or revised c. 800 CE from an earlier text also called the Surya Siddhanta.Now date is arbitrarily assigned as 4/5 Century BC!(According to al-Biruni, the 11th-century Persian scholar and polymath, a text named the Surya Siddhanta was written by one Lāta.The second verse of the first chapter of the Surya Siddhanta attributes the words to an emissary of the solar deity of Hindu mythology, Surya, as recounted to an asura (a mythical being) called Maya at the end of Satya Yuga, the first golden age of Hindu mythology, around two million years ago.Maya has Tamil connection. I shall detail this in another post.The Surya Siddhanta thus consists of cryptic rules in Sanskrit verse. It is a compendium of astronomy that is easier to remember, transmit and use as reference or aid for the experienced, but does not aim to offer commentary, explanation or proof. The text has 14 chapters and 500 shlokas. It is one of the eighteen astronomical siddhanta (treatises), but thirteen of the eighteen are believed to be lost to history. The Surya Siddhanta text has survived since the ancient times, has been the best known and the most referred astronomical text in the Indian tradition. Suryasiddhantha

    References. https://en.m.wikipedia.org/wiki/History_of_mathematics

    Shall write on Vedic Mathematical Structures, to be followed by Tamil concepts on Mathematics.

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  • Laws Of Motion Gravity Trigonometry Hindu Texts

    I have posted some articles on the advanced concepts of Hinduism, some of them are over 5000 years old.

     

    I had recently delivered a lecture on Quantum, Hinduism and the unlocking of natures secrets through Gayatri.

     

    As I was lecturing a senior scientist from a reputed Institution was so upset that when I was proving the inadequacy of Science especially Newton, in explaining many physical events both atomic and in Astrophysics,he interrupted me that None should speak ill of Newton.

     

    My reply from the podium was that when I am talking Vedas and about Shankaracharya, Newton does not come anywhere near and asked the gentleman to wait till I complete the lecture.

     

    I continued with the arguments in the lecture.

     

    I shall deal with the details of the lecture in a separate post.

     

    It is a different matter that the gentlemen met my friend and informed he shall read Sanskrit and Shankara before talking about these issues.

     

    Now let us see in this post what our Vedas and ancient texts say on Laws of Motion,Gravity?

     

    Designing of Spaceships Hindus Sundara Vimana,
    Sundara Vimana,Holo-gravitic buoyancy drive image credit. http://projectavalon.net/forum4/showthread.php?66925-Holo-gravitic-buoyancy-drive

     

    Quote:

     

    The words gravity and gravitational pull are generally translated into Indian
    languages as “GURUTVA AKARSHANA SHAKTI”. The word ‘Gurutva’ means ‘mass’
    and ‘Aakarshana’ means ‘attractive pull’. The very name indicates that the ancient
    Indians observed some relation between the mass of a body and the gravitational pull.

    The Taittiriya branch of Krishna Yajurveda says –

    
        
       
    This means, the sun is holding the earth and the heaven in the space. The sun has
    the power of attraction (kristheeh) and shines without interruption.
    The word “Kristhee” in the above sentence is derived from the root “krish” which
    has no other meaning, but attraction. Saying that the sun is holding the earth in the space
    through his power of attraction, implies that the earth also is a body with a different type
    of force of attraction. Otherwise, if the sun is like a magnetic ball and the earth is like an
    iron ball, they would have collided with each other long back. The same idea is reflected
    very clearly in the following famous Sloka of Varahamihira (6th century AD)

    ….

    The ball of the earth which is made up of the five fundamental elements, is placed
    in the center of a cage, which is made up of the stars of the galaxy and hence it is hanging
    in the sky, like an iron ball in the center of a cage of magnetic balls.

    The word “Panchabhoota Maya” in the above Sloka is important.

    In the context of the solar system, our ancestors did not see the earth as a simple
    mass of mud. The globe of earth, the oceans, the air and the clouds around it put together,
    is treated as “Bhugola”.

    Bhaskaraacharya (12th century AD) made this very clear in his “Goladhyaya” of
    Siddhanta Siromani. ….

    The Surya Siddhanta is one of the earliest doctrines or traditions (siddhanta) in archaeo-astronomy of the Hindus. Its original version is by an unknown author. It describes the archeo-astronomy theories, principles and methods of the ancient Hindus. This siddhanta is supposed to be the knowledge that the Sun god gave to an Asura called Maya. Asuras were enemies of the Deva, the Gods of Hindus. Asuras were believed to be residents of the nether worlds.

    Significant coverage is on kinds of time, length of the year of gods and demons, day and night of god Brahma, the elapsed period since creation, how planets move eastwards and sidereal revolution. The lengths of the Earth’s diameter, circumference are also given. Eclipses and color of the eclipsed portion of the moon is mentioned. This explains the archeo-astronomical basis for the sequence of days of the week named after the Sun, Moon, etc. Musings that there is no above and below and that movement of the starry sphere is left to right for Asuras makes interesting reading.

    Varahamihira in his Panchasiddhantika contrasts it with four other treatises, besides the Paitamaha Siddhantas (which is more similar to the “classical” Vedanga Jyotisha), thePaulisha and Romaka Siddhantas (directly based on Hellenistic astronomy) and the Vasishta Siddhanta. Citation of the Surya Siddhanta is also found in the works of Aryabhata

    The table of contents in this text are:

    1. The Mean Motions of the Planets[notes 1]
    2. True Places of the Planets
    3. Direction, Place and Time
    4. The Moon and Eclipses
    5. The Sun and Eclipses
    6. The Projection of Eclipses
    7. Planetary Conjunctions
    8. Of the Stars
    9. Risings and Settings
    10. The Moon’s Risings and Settings
    11. Certain Malignant Aspects of the Sun and Moon
    12. Cosmogony, Geography, and Dimensions of the Creation
    13. The Gnomon
    14. The Movement of the Heavens and Human Activity.

     

    Trignometry.

    The Surya Siddhanta contains the roots of modern trigonometry. It uses sine (jya), cosine (kojya or “perpendicular sine”) and inverse sine (otkram jya) for the first time, and also contains the earliest use of the tangent and secant when discussing the shadow cast by a gnomon in verses 21–22 of Chapter 3:

    Of [the sun’s meridian zenith distance] find the jya (“base sine”) and kojya (cosine or “perpendicular sine”). If then the jya and radius be multiplied respectively by the measure of the gnomon in digits, and divided by the kojya, the results are the shadow and hypotenuse at mid-day.

    In modern notation, this gives the shadow of the gnomon at midday as

    s = \frac{g \sin \theta}{\cos \theta} = g \tan \theta

    and the hypotenuse of the gnomon at midday as

    h = \frac{g r}{\cos \theta} = g r \frac{1}{\cos \theta} = g r \sec \theta

    where \ g is the measure of the gnomon, \ r is the radius of the gnomon, \ s is the shadow of the gnomon, and \ h is the hypotenuse of the gnomon.

     

    Citations.

     

    Laws of Motion Gravity Hinduism

     

    Surya Siddhanta wiki

     

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