Ramanisblog

Tag: Lalla,

  • 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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  • Twelve Old Astronomical Instruments Of Lalla

    That ancient Indians had advanced concepts in Science especially Astronomy.

    a-sketch-of-some-of-the-instruments-described-by-lalla-e1454322331431
    12 Astronomical Instruments by Lalla.

    Please refer my article on Advanced concepts in Science Hinduism.

    Also the post on Advanced Astronomical instruments India.

    The latter was found in the Surya Siddhanta, which is considered as an authentic source on Astronomy.

    In the earlier article I had written on the Astronomical instruments found.

    Now there is information about another Astronomer , Mathematician Lalla of Gujarat.

    He followed the Surya Siddhanta.

    While the instruments mentioned in the Surya Siddhanta relate to advanced ones, Lalla’s Astronomical Instruments were are meant for daily use.

    ‘

    Despite the significance of Lalla’s work, very little is known about his life. Lalla did not record any dates relating to his life or work in his surviving treatises. He is generally placed in the middle of the eighth century on the basis of his borrowings from earlier authors and those of later authors from him. He followed the tradition of Aryabhata I.  His most important work is the Śiṣyadhīvṛddhida (Treatise Which Expands the Intellect of Students), which, as he says, was composed to expatiate astronomy as set out by Aryabhata. The Śiṣyadhīvṛddhida is in two sections, entitled Grahādhyāya and Golādhyāya.

    The Instruments.

    lalla

     

     

    Golo, bhagana, chakra, dhanu, ghati, shanku, shakata, kartaryaha. Pipta, kapal, shalaka, dwadahsa yantrani saha yastya.

    Translation:

    Sphere, ring, dial, bow, time measuring water vessel. Gnomon, divider, scissor. Circular seat with central stick, semicircle with stick, combination of sticks, are the twelve instuments along with a stick.

    The Gola yantra is a type of armilliary sphere used to locate planetary positions.

    Bhangana is a ring with angular graduations alonge its circumference, it is a type of protractor.

    Chakra is a circular disk with angular graduations, it is also a type of protractor.

    Dhanu is a semicircular disk with angular graduations and a stick pivoted at the center, it is a type of protractor with a plumb bob arrangement.

    Ghati is a small vessel with a hole at the bottom. It was used to measure time.

    Shanku is a type of gnomon, a long vertical cone used to identify East-West-North-South direction based on shadow of its tip.

    A special geometrical construction known a ‘Matsya‘ was used for this purpose. Altitude of sun and day time was also measured with this instrument based on the shadow.

    Shakata consists of two ‘V’ shaped sticks, pivoted at the end.

    Kartari means a seizer. This instrument is made up of two sticks both pivoted together. It was used like a caliper, and also to measure angle with the help of protractor.

    Pitha is a horizontal disk with a vertical stick at its center. It was used to measure local time based on its shadow, it was used to measure the height with the help of special geometrical contruction.

    Shalaka is combination of two sticks with a string.

    Yasti is just a long stick having standard dimensions, it was used to measure height and distances. Special geometrical constructions were framed to facilitate the use of this stick. These proposed geometrical constructions were to construct the proportionate triangles with the help of which heights of terrestrial objects could be calculated.

    Lalla was an eighth-century India.He followed the tradition of Aryabhata I.  His most important work is the Śiṣyadhīvṛddhida (Treatise Which Expands the Intellect of Students), which, as he says, was composed to expatiate astronomy as set out by Aryabhata. The Śiṣyadhīvṛddhida is in two sections, entitled Grahādhyāya and Golādhyāya.  Grahādhyāya deals with planetary calculations, determination of the mean and true planets, three problems pertaining to diurnal motion of Earth, eclipses, rising and setting of the planets, the various cusps of the moon, planetary and astral conjunctions, and complementary situations of the sun and the moon. The second part—titled Golādhyāya deals with graphical representation of planetary motion, astronomical instruments, spherics, and emphasizes on corrections and rejection of flawed principles. It is within Śiṣyadhīvṛddhida that the earliest known description of a perpetuum mobile is described. Lalla also wrote the Jyotiśaratnakośa, a treatise on astrology that survives in the form of several incomplete manuscripts. This work is one of the earliest known Sanskrit astrological works for determining auspicious and inauspicious times. His works were followed by later astronomers Śrīpati, Vateśvara, and Bhaskara II. Lalla also authored the Siddhāntatilaka.

    Citation and reference.

     

    http://www.mysteryofindia.com/2015/11/the-twelve-yantras-of-astronomer-lalla.html