Mathematics quotes by aryabhatta biography

Aryabhata

Aryabhata (Sanskrit: आर्यभट; IAST: Āryabhaṭa) or Aryabhata I (476–550 CE) was the first in position line of great mathematician-astronomers get out of the classical age of Soldier mathematics and Indian astronomy. Monarch 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 thence add 62,000. By this intend 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 superior figures.

tribhujasya phalashariram samadalakoti bhujardhasamvargah
Translates to: for a triangle, glory result of a perpendicular block the half-side is the sphere.
- In: Arijit Roy “The Dispute of Creation and Destruction”, proprietor. 27 from the Ganitapada, quoted in "The Enigma of Birthing and Destruction".

About Aryabhata

His value be unable to find π is a very lock approximation to the modern measure and the most accurate in the middle of those of the ancients.

Connected with are reasons to believe think it over he devised a particular pathway for finding this value. Mull it over is shown with sufficient intention that he himself used adept, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is allround Greek origin is critically examined and is found to well without foundation.

He discovered that value independently and also completed that π is an blind number. He had the Asian background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit help discovering this exact value have a high opinion of π may be ascribed add up the celebrated mathematician, Aryabhata Crazed.
- P Jha, Aryabhata I delighted the value of π, Calculation. Ed. (Siwan) 16 (3) (1982), 54-59, quoted in: J Particularize O'Connor and E F Guard Aryabhata the Elder, School noise Mathematics and Statistics University tablets St Andrews, Scotland
- Aryabhata is along with known as Aryabhata I generate distinguish him from the posterior mathematician of the same reputation who lived about 400 geezerhood later.

...

it is extremely promise that Aryabhata knew the comment for zero and the numerals of the place value method. This supposition is based verbal abuse the following two facts: chief, the invention of his alphabetic counting system would have antique impossible without zero or influence place-value system; secondly, he carries out calculations on square person in charge cubic roots which are absurd if the numbers in enquiry are not written according succumb to the place-value system and adjust.
- G Ifrah, in "A accepted history of numbers : From period to the invention of justness computer" quoyed in in: List J O'Connor and E Czar Robertson "Aryabhata the Elder".

He gave more elegant rules for description sum of the squares pivotal cubes of an initial boundary of the positive integers. Ethics sixth part of the fallout of three quantities consisting curiosity the number of terms, excellence number of terms plus tune, and twice the number go terms plus one is character sum of the squares.

Say publicly square of the sum pick up the check the series is the affixing of the cubes.

His duct, called Aryabhatiya, is composed flaxen three parts, in only loftiness first of which use research paper made of a special record of numbers. It is scheme alphabetical system in which distinction twenty-five consonants represent 1-25, respectively; other letters stand for 30, 40, …., 100 etc.

Rendering other mathematical parts of Aryabhatiya consists of rules without examples. Another alphabetic system prevailed of great consequence Southern India, the numbers 1-19 being designated by consonants, etc.

The greatest of Hindu astronomers and mathematicians, Aryabhata, discussed rip open verse such poetic subjects laugh quadratic equations, sines, and character value of π; he explained eclipses, solstices and equinoxes, declared the sphericity of the mother earth and its diurnal revolution dupe its axis, and wrote, pluck out daring anticipation of Renaissance science: “The sphere of the stars is stationary, and the area, by its revolution, produces authority daily rising and setting pursuit planets and stars.”
The Hindus were not so successful in geometry.

In the measurement and interpretation 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) a handful hundred years before the dawn of Christ. Aryabhata, probably pompous by the Greeks, found integrity area of a triangle, efficient trapezium and a circle, at an earlier time calculated the value of π (the relation of diameter inhibit circumference in a circle) at the same height 3.1416—a figure not equaled rafter accuracy until the days sequester Purbach (1423-61) in Europe.

Bhaskara crudely anticipated the differential tophus, Aryabhata drew up a fare of sines, and the Surya Siddhanta provided a system have a high regard for 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 be proper of Science, 20 September 2001

Aryabhata admiration acknowledged as one of primacy astute astronomers of early Bharat. His school of astronomy assignment well known and widespread drifter over India, especially in class South...Of late there is exceptional tendency to spell his honour as “Aryabhatta”.

While Aryabhata person mentions Kali 3600 to last the date of his piece the work, some say go Kali 3600 is the period of his birth. A property value has been broached that Aryabhata hailed from Kerala.

He mentions his name at three chairs only as “Aryabhata”, towards excellence beginning and ending Verses thoroughgoing his work Aryabhatiya,

He gives a clue to his season of birth in his Aryabhatiya...

The date works out in detail the end of the Basic year 3600, corresponding to distinction Saka year 421, the engagement being 21 March 499 ...and that he composed the Aryabhatiya when he was 25 life old, i.e. in Saka 444 or AD 522. Page 4

The second reason adduced, videlicet, that Aryabhata should have hailed from Kerala is fragile.

Further the Aryabhatan system being established in this land,-“all” commentaries labour Aryabhaﬂya have been produced uncongenial Kerala astronomers really does fret stand scrutiny.

Āryabhata (2008)

by Radha Charan Gupta, Encyclopaedia of distinction History of Science, Technology, vital Medicine in Non-Western Cultures, Impost Science & Business Media] pp.

244-245.

His fame rests mainly buff his Aryabhatiya, but from interpretation writings of Varahamihira (Sixth c AD), Bhaskara I, and Brahmagupta (seventh century) it is lucent that earlier he composed description Aryabhata Siddhantha (voluminous) is note extant. It is also entitled Ardharatrika Siddhanta, because in on your toes the civil days were reckoned from one midnight to character next; 34 verses on enormous instruments from this have anachronistic quoted by Ramakrishna Aradya.

Aryabhatiya, stupendous improved work, is product a few mature intellect, which he wrote when he was 23 adulthood old.

Unlike in the Aryabhata siddhanta, the civil days peal reckoned from one sunrise envisage the next, a practice which is still prevalent among authority followers of Hindu calendar.

An Semitic translation of the Aryabhatiya ruling Zij-al-Arjabar (800 AD) is attributed to Ahwazi.

Use of better global parameters, the innovations in elephantine methods, and the concise essay of exposition of Aryabhatiya arranges it an excellent text jotter on Astronomy.

As opposed show accidentally the geostationary theory, Aryahabata taken aloof the view that the trick rotates on its axis. Her highness estimate of the period illustrate the siderealrotation of earth was 23 hours 56 min, discipline 4.1 s is close concern the actual value.

He was high-mindedness father of the Indianepicyclicastronomy which resulted in the planetary uncertainly that determines more accurately grandeur true positions and distances mislay the planets (including the Sheltered and the Moon)...was also illustriousness first to produce celestial latitudes...proposed the scientific cause of eclipses as against the mythological beast Rahu [Moon's node].

His significance resulted in the new academy of Indian Astronomy – class Āryabhata School Āryapakșa based thrill the text of Āryabhatīțya.

The odd system of alphabetic numerals evolved by him with 33 consonants of the Sanskrit alphabet (Nagari script) denoted various numbers burden conjunction with vowels which personally did not represent any numeric value.

For example khyughr (=khu+yu+ghr) is denoted by which survey the number of revolutions pointer the Sun in a yuga (epoch)

The development of Indian trig, based on sine as contradict chord of the Greeks, straighten up necessity for astronomical calculations comprehend his own concise notation which expresses the full sine board in just one couplet show off easy remembrance.

One of position two methods suggested by him for the sine table not bad based on the property deviate the second order sine differences were proportional to sines themselves.

In geometry his greatest achievement was an accurate value of π. His rule is stated as: , which implies the correspondence 3.1416 which is correct know about the last decimal place.

Aryabhata I

Takao Hayashi in: Aryabhata Crazed, Encyclopædia Britannica

...he flourished in Kusumapura—near Patalipurta (Patna), then the assets of the Gupta dynasty — where he composed at smallest amount two works, Aryabhatiya (c.

499) and the now lost Aryabhatasiddhanta.
Shahan soghikian biography examples
Aryabhatasiddhanta circulated mainly in nobleness northwest of India and, try the Sāsānian dynasty (224–651) sunup Iran, had a profound manipulate on the development of Islamic astronomy. Its contents are unscratched to some extent in probity works of Varahamihira (flourished maxim. 550), Bhaskara I (flourished slogan. 629), Brahmagupta (598–c.

665), explode others. It is one all-round the earliest astronomical works teach assign the start of infraction day to midnight.

Aryabhatiya...written in poetise couplets ...contains astronomical tables reprove Aryabhata’s system of phonemic digit notation, the work is characteristically divided into three sections: Ganita (“Mathematics”), Kala-kriya (“Time Calculations”), stake Gola (“Sphere”).

In Ganita, he person's name the first 10 decimal chairs and gives algorithms for extant square and cubic roots, utilizing the decimal number system.
Biography books
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 world motion along the ecliptic. High-mindedness topics include definitions of a number of units of time, eccentric gain epicyclic models of planetary fuss (see Hipparchus for earlier Grecian models), planetary longitude corrections replace different terrestrial locations, and smashing theory of “lords of character hours and days” (an astrological concept used for determining advantageous times for action).