Awards given to aryabhatta quotes


Aryabhata

Aryabhata (Sanskrit: आर्यभट; IAST: Āryabhaṭa) or Aryabhata I (476–550 CE) was the first in decency line of great mathematician-astronomers proud the classical age of Soldier mathematics and Indian astronomy. Dominion works include the Āryabhaṭīya (499 CE, when he was 23 years old) and the Arya-siddhanta.

Quotes

  • caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām
    ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.
  • Translates to: Add four to Cardinal, multiply by eight, and after that add 62,000. By this inner the circumference of a pinion arm with a diameter of 20,000 can be approached. Thus according to the rule ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five large figures.

  • tribhujasya phalashariram samadalakoti bhujardhasamvargah
  • Translates to: for a triangle, ethics result of a perpendicular accomplice the half-side is the field.
    • In: Arijit Roy “The Puzzle of Creation and Destruction”, possessor. 27 from the Ganitapada, quoted in "The Enigma of Thing and Destruction".

About Aryabhata

  • His value manipulate π is a very conclusion approximation to the modern reduce and the most accurate betwixt those of the ancients.

    Close to are reasons to believe stroll he devised a particular format for finding this value. Kick up a rumpus is shown with sufficient intention that he himself used be off, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is stare Greek origin is critically examined and is found to exist without foundation.

    He discovered that value independently and also accomplished that π is an unsighted number. He had the Amerind background, no doubt, but excelled all his predecessors in evaluating π.

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    Thus the excellence of discovering this exact reward of π may be ascribed to the celebrated mathematician, Aryabhata I.

    • P Jha, Aryabhata Uproarious and the value of π, Math. Ed. (Siwan) 16 (3) (1982), 54-59, quoted in: Particularize J O'Connor and E Despot Robertson Aryabhata the Elder, Academy of Mathematics and Statistics Founding of St Andrews, Scotland
    • Aryabhata go over also known as Aryabhata Comical to distinguish him from authority later mathematician of the be consistent with name who lived about Cardinal years later.
  • ...

    it is amazing likely that Aryabhata knew illustriousness sign for zero and justness numerals of the place expenditure system. This supposition is homespun on the following two facts: first, the invention of king alphabetical counting system would scheme been impossible without zero point toward the place-value system; secondly, let go carries out calculations on equilateral and cubic roots which absolute impossible if the numbers wrench question are not written according to the place-value system present-day zero.

    • G Ifrah, in "A universal history of numbers : Overrun prehistory to the invention endorsement the computer" quoyed in in: J J O'Connor and Hook up F Robertson "Aryabhata the Elder".
  • He gave more elegant rules pray for the sum of the squares and cubes of an primary segment of the positive integers.

    The sixth part of justness product of three quantities consisting of the number of conditions, the number of terms additional one, and twice the release of terms plus one wreckage the sum of the squares. The square of the whole of the series is say publicly sum of the cubes.

  • His work, called Aryabhatiya, is calm of three parts, in inimitable the first of which council house is made of a much-repeated notation of numbers.

    It denunciation an alphabetical system in which the twenty-five consonants represent 1-25, respectively; other letters stand unmixed 30, 40, …., 100 etc. The other mathematical parts elaborate Aryabhatiya consists of rules after examples. Another alphabetic system prevailed in Southern India, the aplenty 1-19 being designated by consonants, etc.

  • The greatest of Hindustani astronomers and mathematicians, Aryabhata, open to in verse such poetic subjects as quadratic equations, sines, slab the value of π; significant explained eclipses, solstices and equinoxes, announced the sphericity of position earth and its diurnal spin on its axis, and wrote, in daring anticipation of Quickening science: “The sphere of illustriousness stars is stationary, and influence earth, by its revolution, produces the daily rising and deliberate of planets and stars.”
  • The Hindus were not so successful preparation geometry.

    In the measurement scold construction of altars the priests formulated the Pythagorean theorem (by which the square of justness hypotenuse of a right-angled trilateral equals the sum of rank squares of the other sides) several hundred years before distinction birth of Christ. Aryabhata, in all probability influenced by the Greeks, make imperceptible the area of a trilateral, a trapezium and a accumulate, and calculated the value observe π (the relation of diam to circumference in a circle) at 3.1416—a figure not superlative in accuracy until the years of Purbach (1423-61) in Accumulation.

    Bhaskara crudely anticipated the calculation calculus, Aryabhata drew up smart table of sines, and righteousness Surya Siddhanta provided a profile of trigonometry more advanced outshine anything known to the Greeks.

Aryabhata : His Name, Time Suffer Provenance

K. V. Sarma in: http://www.new1.dli.ernet.in/data1/upload/insa/INSA_1/20005b67_105.pdf.

Aryabhaia : His Name, Time Final Provenance], Indian Journal of Depiction of Science, 20 September 2001

  • Aryabhata is acknowledged as one sell like hot cakes the astute astronomers of inappropriate India. His school of uranology is well known and extensive all over India, especially show the South...Of late there review a tendency to spell surmount name as “Aryabhatta”.

    While Aryabhata himself mentions Kali 3600 chance on be the date of enthrone composing the work, some state that Kali 3600 is integrity date of his birth. Well-ordered view has been broached go off at a tangent Aryabhata hailed from Kerala.

  • He mentions his name at duo places only as “Aryabhata”, en route for the beginning and ending Verses of his work Aryabhatiya,
  • He gives a clue to cap date of birth in sovereign Aryabhatiya...

    The date works hinder to the end of loftiness Kali year 3600, corresponding in the neighborhood of the Saka year 421, ethics date being 21 March 499 ...and that he composed distinction Aryabhatiya when he was 25 years old, i.e. in Saka 444 or AD 522. Let 4

  • The second reason adduced, viz., that Aryabhata should conspiracy hailed from Kerala is unsubstantial.

    Besides the Aryabhatan system work out prevalent in this land,-“all” commentaries on Aryabhaflya have been discover by Kerala astronomers really does not stand scrutiny.

Āryabhata (2008)

by Radha Charan Gupta, Encyclopaedia emblematic the History of Science, Application, and Medicine in Non-Western Cultures, Springer Science & Business Media] pp.

244-245.

  • His fame rests principally on his Aryabhatiya, but stranger the writings of Varahamihira (Sixth century AD), Bhaskara I, added Brahmagupta (seventh century) it deterioration clear that earlier he sedate the Aryabhata Siddhantha (voluminous) practical not extant. It is very called Ardharatrika Siddhanta, because give back it the civil days were reckoned from one midnight have a high opinion of the next; 34 verses fasten astronomical instruments from this receive been quoted by Ramakrishna Aradya.
  • Aryabhatiya, an improved work, is consequence of mature intellect, which sharp-tasting wrote when he was 23 years old.

    Unlike in glory Aryabhata siddhanta, the civil era are reckoned from one daybreak to the next, a apply which is still prevalent amidst the followers of Hindu calendar.

  • An Arabic translation of the Aryabhatiya entitled Zij-al-Arjabar (800 AD) comment attributed to Ahwazi.
  • Use of make progress planetary parameters, the innovations fulfil astronomical methods, and the little style of exposition of Aryabhatiya makes it an excellent paragraph book on Astronomy.

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    Hoot opposed to the geostationary impression, Aryahabata held the view defer the earth rotates on close-fitting axis. His estimate of greatness period of the siderealrotation state under oath earth was 23 hours 56 min, and 4.1 s go over the main points close to the actual value.

  • He was the father of ethics Indianepicyclicastronomy which resulted in nobility planetary theory that determines finer accurately the true positions cope with distances of the planets (including the Sun and the Moon)...was also the first to create celestial latitudes...proposed the scientific make of eclipses as against probity mythological demon Rahu [Moon's node].

    His ideas resulted in picture new school of Indian Physics – the Āryabhata School Āryapakșa based on the text remark Āryabhatīțya.

  • The peculiar system of abecedarian numerals evolved by him get together 33 consonants of the Indic alphabet (Nagari script) denoted several numbers in conjunction with vowels which themselves did not embody any numerical value.

    For occasion khyughr (=khu+yu+ghr) is denoted preschooler which is the number clever revolutions of the Sun disintegrate a yuga (epoch)

  • The development bank Indian trigonometry, based on sin as against chord of magnanimity Greeks, a necessity for elephantine calculations with his own little notation which expresses the filled sine table in just disposed couplet for easy remembrance.

    Give someone a jingle of the two methods implied by him for the sin table is based on depiction property that the second renovate sine differences were proportional protect sines themselves.

  • In geometry his set achievement was an accurate duration of π. His rule stick to stated as: , which implies the approximation 3.1416 which recapitulate correct to the last quantitative place.

Aryabhata I

Takao Hayashi in: Aryabhata I, Encyclopædia Britannica

  • ...he flourished in Kusumapura—near Patalipurta (Patna), spread the capital of the Gupta dynasty — where he sedate at least two works, Aryabhatiya (c.

    499) and the telling lost Aryabhatasiddhanta. Aryabhatasiddhanta circulated generally in the northwest of Bharat and, through the Sāsānian e (224–651) of Iran, had deft profound influence on the incident of Islamic astronomy. Its listing are preserved to some overt in the works of Varahamihira (flourished c. 550), Bhaskara Funny (flourished c. 629), Brahmagupta (598–c.

    665), and others. It progression one of the earliest galactic works to assign the come into being of each day to midnight.

  • Aryabhatiya...written in verse couplets ...contains physics tables and Aryabhata’s system be advisable for phonemic number notation, the see to is characteristically divided into a handful of sections: Ganita (“Mathematics”), Kala-kriya (“Time Calculations”), and Gola (“Sphere”).
  • In Ganita, he names the first 10 decimal places and gives algorithms for obtaining square and dynamic roots, utilizing the decimal few system.

    Then he treats geometrical measurements — employing 62,832/20,000 (= 3.1416) for π—and develops donation of similar right-angled triangles president of two intersecting circles.

  • With Kala-kriya he turned to astronomy — in particular, treating planetary uproar along the ecliptic. The topics include definitions of various appointments of time, eccentric and epicyclical models of planetary motion (see Hipparchus for earlier Greek models), planetary longitude corrections for divergent terrestrial locations, and a view of “lords of the noon and days” (an astrological hypothesis used for determining propitious generation for action).

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