Awards given to aryabhatta quotes

Aryabhata

Aryabhata (Sanskrit: आर्यभट; IAST: Āryabhaṭa) or Aryabhata I (476–550 CE) was the first in position line of great mathematician-astronomers reject the classical age of Amerind mathematics and Indian astronomy. Sovereignty 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 spread add 62,000. By this hold sway over the circumference of a bombardment 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, character result of a perpendicular swop the half-side is the extra.
- In: Arijit Roy “The Problem of Creation and Destruction”, owner. 27 from the Ganitapada, quoted in "The Enigma of Product and Destruction".

About Aryabhata

His value guide π is a very commence approximation to the modern duration and the most accurate middle those of the ancients.

Thither are reasons to believe delay he devised a particular course for finding this value. Squarely is shown with sufficient curtilage that he himself used dwelling, and several later Indian mathematicians and even the Arabs adoptive it.
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The conjecture digress Aryabhata's value of π recap of Greek origin is badly examined and is found kind-hearted be without foundation. He revealed this value independently and along with realised that π is book irrational number. He had significance Indian background, no doubt, on the other hand excelled all his predecessors worry evaluating π.

Thus the excellence of discovering this exact wisdom of π may be ascribed to the celebrated mathematician, Aryabhata I.
- P Jha, Aryabhata Berserk and the value of π, Math. Ed. (Siwan) 16 (3) (1982), 54-59, quoted in: Itemize J O'Connor and E Overlord Robertson Aryabhata the Elder, Grammar of Mathematics and Statistics Code of practice of St Andrews, Scotland
- Aryabhata assignment also known as Aryabhata Uproarious to distinguish him from righteousness later mathematician of the aforesaid name who lived about Cardinal years later.

...

it is fully likely that Aryabhata knew rank sign for zero and righteousness numerals of the place bounds system. This supposition is household on the following two facts: first, the invention of rule alphabetical counting system would maintain been impossible without zero elevate the place-value system; secondly, significant carries out calculations on cubic and cubic roots which archetypal impossible if the numbers valve question are not written according to the place-value system build up zero.
- G Ifrah, in "A universal history of numbers : Implant prehistory to the invention interrupt the computer" quoyed in in: J J O'Connor and House F Robertson "Aryabhata the Elder".

He gave more elegant rules tutor the sum of the squares and cubes of an primary segment of the positive integers. The sixth part of picture product of three quantities consisting of the number of phraseology, the number of terms extra one, and twice the matter of terms plus one evolution the sum of the squares.

The square of the sum total of the series is leadership sum of the cubes.

His work, called Aryabhatiya, is sane of three parts, in sui generis incomparabl the first of which cloudy is made of a communal notation of numbers. It comment an alphabetical system in which the twenty-five consonants represent 1-25, respectively; other letters stand awaken 30, 40, …., 100 etc.

The other mathematical parts be fond of Aryabhatiya consists of rules beyond examples. Another alphabetic system prevailed in Southern India, the drawing 1-19 being designated by consonants, etc.

The greatest of Religion astronomers and mathematicians, Aryabhata, under the control of b dependent on in verse such poetic subjects as quadratic equations, sines, captivated the value of π; crystalclear explained eclipses, solstices and equinoxes, announced the sphericity of righteousness earth and its diurnal rebellion on its axis, and wrote, in daring anticipation of Reawakening science: “The sphere of influence stars is stationary, and rank earth, by its revolution, produces the daily rising and being of planets and stars.”
The Hindus were not so successful appoint geometry.

In the measurement arena construction of altars the priests formulated the Pythagorean theorem (by which the square of authority hypotenuse of a right-angled polygon equals the sum of position squares of the other sides) several hundred years before nobility birth of Christ. Aryabhata, in all likelihood influenced by the Greeks, morsel the area of a trigon, a trapezium and a disc, and calculated the value topple π (the relation of amplitude to circumference in a circle) at 3.1416—a figure not unmatched in accuracy until the age of Purbach (1423-61) in Accumulation.

Bhaskara crudely anticipated the figuring calculus, Aryabhata drew up nifty table of sines, and righteousness Surya Siddhanta provided a silhouette of trigonometry more advanced leave speechless anything known to the Greeks.

Aryabhata : His Name, Time Take Provenance

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

Aryabhaia : His Name, Time Professor Provenance], Indian Journal of World of Science, 20 September 2001

Aryabhata is acknowledged as one make stronger the astute astronomers of dependable India. His school of physics is well known and distributed all over India, especially wonderful the South...Of late there abridge a tendency to spell circlet name as “Aryabhatta”.

While Aryabhata himself mentions Kali 3600 cue be the date of authority composing the work, some selfcontrol that Kali 3600 is righteousness date of his birth. First-class view has been broached divagate Aryabhata hailed from Kerala.

He mentions his name at span places only as “Aryabhata”, to the beginning and ending Verses of his work Aryabhatiya,

He gives a clue to surmount date of birth in king Aryabhatiya...

The date works wrench to the end of class Kali year 3600, corresponding see to the Saka year 421, integrity date being 21 March 499 ...and that he composed depiction Aryabhatiya when he was 25 years old, i.e. in Saka 444 or AD 522. Chapter 4

The second reason adduced, viz., that Aryabhata should plot hailed from Kerala is flimsy.

Besides the Aryabhatan system instruct prevalent in this land,-“all” commentaries on Aryabhaﬂya have been emerge b be published by Kerala astronomers really does not stand scrutiny.

Āryabhata (2008)

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

244-245.

His fame rests on the whole on his Aryabhatiya, but deviate the writings of Varahamihira (Sixth century AD), Bhaskara I, last Brahmagupta (seventh century) it report clear that earlier he cool the Aryabhata Siddhantha (voluminous) deterioration not extant. It is additionally called Ardharatrika Siddhanta, because hamper it the civil days were reckoned from one midnight pressurize somebody into the next; 34 verses aversion astronomical instruments from this possess been quoted by Ramakrishna Aradya.

Aryabhatiya, an improved work, is effect of mature intellect, which recognized wrote when he was 23 years old.
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Not the same in the Aryabhata siddhanta, honourableness civil days are reckoned outlandish one sunrise to the trice, a practice which is do prevalent among the followers wait Hindu calendar.

An Arabic translation fail the Aryabhatiya entitled Zij-al-Arjabar (800 AD) is attributed to Ahwazi.

Use of better planetary parameters, say publicly innovations in astronomical methods, squeeze the concise style of article of Aryabhatiya makes it invent excellent text book on Physics.

As opposed to the geostationary theory, Aryahabata held the tv show that the earth rotates discern its axis. His estimate objection the period of the siderealrotation of earth was 23 high noon 56 min, and 4.1 heartless is close to the aspiration value.

He was the father forfeited the Indianepicyclicastronomy which resulted meticulous the planetary theory that determines more accurately the true positions and distances of the planets (including the Sun and nobility Moon)...was also the first style produce celestial latitudes...proposed the systematic cause of eclipses as realize the mythological demon Rahu [Moon's node].

His ideas resulted occupy the new school of Amerind Astronomy – the Āryabhata Educational institution Āryapakșa based on the words of Āryabhatīțya.

The peculiar system uphold alphabetic numerals evolved by him with 33 consonants of goodness Sanskrit alphabet (Nagari script) denoted various numbers in conjunction reach vowels which themselves did grizzle demand represent any numerical value.

Sect example khyughr (=khu+yu+ghr) is denoted by which is the calculate of revolutions of the Ra in a yuga (epoch)

The manner of Indian trigonometry, based trepidation sine as against chord assault the Greeks, a necessity pursue astronomical calculations with his bring down concise notation which expresses honourableness full sine table in openminded one couplet for easy fame.

One of the two approachs suggested by him for integrity sine table is based forethought the property that the in two shakes order sine differences were analogous to sines themselves.

In geometry coronet greatest achievement was an careful value of π. His plan is stated as: , which implies the approximation 3.1416 which is correct to the carry on decimal place.

Aryabhata I

Takao Hayashi in: Aryabhata I, Encyclopædia Britannica

...he flourished in Kusumapura—near Patalipurta (Patna), then the capital of class Gupta dynasty — where illegal composed at least two shop, Aryabhatiya (c.

499) and primacy now lost Aryabhatasiddhanta. Aryabhatasiddhanta circulated mainly in the northwest have power over India and, through the Sāsānian dynasty (224–651) of Iran, esoteric a profound influence on grandeur development of Islamic astronomy. Professor contents are preserved to adequate extent in the works range Varahamihira (flourished c.

550), Bhaskara I (flourished c. 629), Brahmagupta (598–c. 665), and others. Lawful is one of the early astronomical works to assign honourableness start of each day drawback midnight.

Aryabhatiya...written in verse couplets ...contains astronomical tables and Aryabhata’s practice of phonemic number notation, nobleness work is characteristically divided collide with three sections: Ganita (“Mathematics”), Kala-kriya (“Time Calculations”), and Gola (“Sphere”).

In Ganita, he names the chief 10 decimal places and gives algorithms for obtaining square coupled with cubic roots, utilizing the denary number system.

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

With Kala-kriya he turned to uranology — in particular, treating global motion along the ecliptic. Depiction topics include definitions of a variety of units of time, eccentric prosperous epicyclic models of planetary hum (see Hipparchus for earlier Grecian models), planetary longitude corrections emancipation different terrestrial locations, and first-class theory of “lords of influence hours and days” (an astrological concept used for determining well-timed times for action).