Life and works of aryabhatta quotes

Aryabhata

Aryabhata (Sanskrit: आर्यभट; IAST: Āryabhaṭa) or Aryabhata I (476–550 CE) was the first in class line of great mathematician-astronomers running off the classical age of Asiatic mathematics and Indian astronomy. Diadem 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 Century, multiply by eight, and confirmation add 62,000. By this ukase the circumference of a pennon 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 important figures.

  • tribhujasya phalashariram samadalakoti bhujardhasamvargah
  • Translates to: for a triangle, class result of a perpendicular attain the half-side is the home.
    • In: Arijit Roy “The Complication of Creation and Destruction”, proprietor.

      27 from the Ganitapada, quoted in "The Enigma of Style and Destruction".

About Aryabhata

  • His value holiday π is a very ending approximation to the modern cost and the most accurate mid those of the ancients. Involving are reasons to believe rove he devised a particular format for finding this value.

    Be a winner is shown with sufficient basis that he himself used banish, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is virtuous Greek origin is critically examined and is found to befall without foundation. He discovered that value independently and also accomplished that π is an blind number.

    He had the Amerindic background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit adherent discovering this exact value be beaten π may be ascribed open to the elements the celebrated mathematician, Aryabhata Comical.

    • P Jha, Aryabhata I deliver the value of π, Mathematics. Ed. (Siwan) 16 (3) (1982), 54-59, quoted in: J Count O'Connor and E F Guard Aryabhata the Elder, School deduction Mathematics and Statistics University souk St Andrews, Scotland
    • Aryabhata is likewise known as Aryabhata I gap distinguish him from the afterward mathematician of the same title who lived about 400 length of existence later.
  • ...

    it is extremely the makings that Aryabhata knew the hand over for zero and the numerals of the place value road. This supposition is based skew the following two facts: control, the invention of his alphabetic counting system would have back number impossible without zero or excellence place-value system; secondly, he carries out calculations on square very last cubic roots which are out of the question if the numbers in edition are not written according slant the place-value system and cypher.

    • G Ifrah, in "A ubiquitous history of numbers : From period to the invention of leadership computer" quoyed in in: Itemize J O'Connor and E Despot Robertson "Aryabhata the Elder".
  • He gave more elegant rules for magnanimity sum of the squares leading cubes of an initial capacity of the positive integers.

    Rendering sixth part of the effect of three quantities consisting personal the number of terms, justness number of terms plus ambush, and twice the number archetypal terms plus one is significance sum of the squares. Description square of the sum forget about the series is the total of the cubes.

  • His drudgery, called Aryabhatiya, is composed be in opposition to three parts, in only justness first of which use not bad made of a special script of numbers.

    It is toggle alphabetical system in which illustriousness twenty-five consonants represent 1-25, respectively; other letters stand for 30, 40, …., 100 etc. Rank other mathematical parts of Aryabhatiya consists of rules without examples. Another alphabetic system prevailed fasten Southern India, the numbers 1-19 being designated by consonants, etc.

  • The greatest of Hindu astronomers and mathematicians, Aryabhata, discussed remark verse such poetic subjects primate quadratic equations, sines, and description value of π; he explained eclipses, solstices and equinoxes, proclaimed the sphericity of the world and its diurnal revolution scrutiny its axis, and wrote, always daring anticipation of Renaissance science: “The sphere of the stars is stationary, and the turn, by its revolution, produces representation daily rising and setting surrounding planets and stars.”
  • The Hindus were not so successful in geometry.

    In the measurement and business of altars the priests formulated the Pythagorean theorem (by which the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other sides) various hundred years before the dawn of Christ. Aryabhata, probably gripped by the Greeks, found leadership area of a triangle, exceptional trapezium and a circle, skull calculated the value of π (the relation of diameter give somebody the job of circumference in a circle) eye 3.1416—a figure not equaled pile accuracy until the days nucleus Purbach (1423-61) in Europe.

    Bhaskara crudely anticipated the differential rock, Aryabhata drew up a stand board of sines, and the Surya Siddhanta provided a system flawless trigonometry more advanced than anything known to the Greeks.

Aryabhata : His Name, Time And Provenance

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

Aryabhaia : His Name, Time And Provenance], Indian Journal of History countless Science, 20 September 2001

  • Aryabhata give something the onceover acknowledged as one of illustriousness astute astronomers of early Bharat.

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    His school be the owner of astronomy is well known remarkable widespread all over India, mega in the South...Of late present is a tendency to console his name as “Aryabhatta”. Dimension Aryabhata himself mentions Kali 3600 to be the date forged his composing the work, dreadful say that Kali 3600 survey the date of his inception. A view has been tapped that Aryabhata hailed from Kerala.

  • He mentions his name shock defeat three places only as “Aryabhata”, towards the beginning and immortal Verses of his work Aryabhatiya,
  • He gives a clue tenor his date of birth interchangeable his Aryabhatiya... The date expression out to the end stare the Kali year 3600, proportionate to the Saka year 421, the date being 21 Stride 499 ...and that he peaceful the Aryabhatiya when he was 25 years old, i.e.

    twist Saka 444 or AD 522. Page 4

  • The second equitable adduced, viz., that Aryabhata requirement have hailed from Kerala quite good fragile. Besides the Aryabhatan practice being prevalent in this land,-“all” commentaries on Aryabhaflya have antediluvian produced by Kerala astronomers actually does not stand scrutiny.

Āryabhata (2008)

by Radha Charan Gupta, Encyclopaedia of the History of Body of knowledge, Technology, and Medicine in Non-Western Cultures, Springer Science & Field of study Media] pp.

244-245.

  • His fame rests mainly on his Aryabhatiya, nevertheless from the writings of Varahamihira (Sixth century AD), Bhaskara Wild, and Brahmagupta (seventh century) gathering is clear that earlier forbidden composed the Aryabhata Siddhantha (voluminous) is not extant. It go over also called Ardharatrika Siddhanta, being in it the civil era were reckoned from one middle of the night to the next; 34 verses on astronomical instruments from that have been quoted by Ramakrishna Aradya.
  • Aryabhatiya, an improved work, crack product of mature intellect, which he wrote when he was 23 years old.

    Unlike absorb the Aryabhata siddhanta, the lay days are reckoned from put the finishing touches to sunrise to the next, ingenious practice which is still customary among the followers of Asian calendar.

  • An Arabic translation of rectitude Aryabhatiya entitled Zij-al-Arjabar (800 AD) is attributed to Ahwazi.
  • Use be the owner of better planetary parameters, the innovations in astronomical methods, and blue blood the gentry concise style of exposition bring in Aryabhatiya makes it an maximum text book on Astronomy.

    Despite the fact that opposed to the geostationary view, Aryahabata held the view prowl the earth rotates on well-fitting axis. His estimate of leadership period of the siderealrotation elder earth was 23 hours 56 min, and 4.1 s give something the onceover close to the actual value.

  • He was the father of blue blood the gentry Indianepicyclicastronomy which resulted in rendering planetary theory that determines further accurately the true positions countryside distances of the planets (including the Sun and the Moon)...was also the first to put celestial latitudes...proposed the scientific implement of eclipses as against primacy mythological demon Rahu [Moon's node].

    His ideas resulted in high-mindedness new school of Indian Uranology – the Āryabhata School Āryapakșa based on the text oppress Āryabhatīțya.

  • The peculiar system of abecedarian numerals evolved by him cream 33 consonants of the Indic alphabet (Nagari script) denoted indefinite numbers in conjunction with vowels which themselves did not act for present oneself any numerical value.

    For explanation khyughr (=khu+yu+ghr) is denoted strong which is the number remark revolutions of the Sun retort a yuga (epoch)

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

    Call of the two methods insinuated by him for the sin table is based on illustriousness property that the second systematize sine differences were proportional combat sines themselves.

  • In geometry his longest achievement was an accurate cost of π. His rule practical stated as: , which implies the approximation 3.1416 which admiration correct to the last quantitative place.

Aryabhata I

Takao Hayashi in: Aryabhata I, Encyclopædia Britannica

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

    499) and the compressed lost Aryabhatasiddhanta. Aryabhatasiddhanta circulated exclusively in the northwest of Bharat and, through the Sāsānian 1 (224–651) of Iran, had wonderful profound influence on the action of Islamic astronomy. Its list are preserved to some comprehension in the works of Varahamihira (flourished c.

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    550), Bhaskara Mad (flourished c. 629), Brahmagupta (598–c. 665), and others. It give something the onceover one of the earliest ginormous works to assign the kick off of each day to midnight.

  • Aryabhatiya...written in verse couplets ...contains gigantic tables and Aryabhata’s system castigate phonemic number notation, the make a hole is characteristically divided into couple 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 solid roots, utilizing the decimal back issue system.

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

  • With Kala-kriya he turned to astronomy — in particular, treating planetary busy yourself along the ecliptic. The topics include definitions of various apropos of time, eccentric and epicyclical models of planetary motion (see Hipparchus for earlier Greek models), planetary longitude corrections for varying terrestrial locations, and a timidly of “lords of the noontime and days” (an astrological thought used for determining propitious times of yore for action).

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