Wikipedia aryabhatta contribution

In Aryabhatiya, Aryabhatta introduced a system of numerals in which he used letters of the Indian alphabet to denote numbers. His numeral system allowed numbers up to 10 18 to be represented with an alphabetical notation. It is considered that Aryabhatta was familiar with the concept of zero and the place value system. By this rule, the circumference of a circle with a diameter of 20, can be approached.

Furthermore, it is also considered that Aryabhata knew that the value of Pi was irrational. This was an amazing discovery since the value of Pi was proved to be irrational only in the year by Swiss mathematician Johann Heinrich Lambert. Aryabhata calculated the circumference of the Earth as 39, kilometers while the actual circumference is 40, kilometers.

Aryabhata also put forth impressive calculations regarding the sidereal rotation rotation calculated by referencing the position of the fixed stars of the Earth. He calculated it as 23 hours, 56 minutes and 4. Similarly, Aryabhata calculated the value of the sidereal year to be These calculations by Aryabhatta were one of the most accurate calculations in the world till that time.

Even with the lack of any accurate astronomical instruments at the time, Aryabhata was able to successfully deduce that the Earth is round and revolves around its axis. Furthermore, he connected this with the existence of the day and night. Aryabhata used a geocentric model for the solar system, in which the Sun and Moon are each carried by epicycles which in turn revolve around the Earth.

However, despite using a geocentric model, Aryabhata correctly explained how the moons and planets have no light of their own but shine due to the reflection of sunlight. Furthermore he corrected the flawed belief that eclipses are caused because of the shadows cast by the Earth and Moon and instead explained the correct causes of eclipses.

This supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the place-value system; secondly, he carries out calculations on square and cubic roots which are impossible if the numbers in question are not written according to the place-value system and zero.

The problem arose from studying the problem in astronomy of determining the periods of the planets. Aryabhata uses the kuttaka method to solve problems of this type. The word kuttaka means "to pulverise" and the method consisted of breaking the problem down into new problems where the coefficients became smaller and smaller with each step.

The method here is essentially the use of the Euclidean algorithm to find the highest common factor of a a a and b b b but is also related to continued fractions. By this rule the relation of the circumference to diameter is given. Aryabhata does not explain how he found this accurate value but, for example, Ahmad [ 5 ] considers this value as an approximation to half the perimeter of a regular polygon of sides inscribed in the unit circle.

However, in [ 9 ] Bruins shows that this result cannot be obtained from the doubling of the number of sides. There are reasons to believe that Aryabhata devised a particular method for finding this value. It is shown with sufficient grounds that Aryabhata himself used it, and several later Indian mathematicians and even the Arabs adopted it.

We now look at the trigonometry contained in Aryabhata's treatise. Other rules given by Aryabhata include that for summing the first n n n integers, the squares of these integers and also their cubes. Aryabhata gives formulae for the areas of a triangle and of a circle which are correct, but the formulae for the volumes of a sphere and of a pyramid are claimed to be wrong by most historians.

He also appears to give an incorrect expression for the volume of a sphere. However, as is often the case, nothing is as straightforward as it appears and Elfering see for example [ 13 ] argues that this is not an error but rather the result of an incorrect translation. However, in his translation Elfering translates two technical terms in a different way to the meaning which they usually have.

Without some supporting evidence that these technical terms have been used with these different meanings in other places it would still appear that Aryabhata did indeed give the incorrect formulae for these volumes. Aryabhata gives a systematic treatment of the position of the planets in space. He believed that the apparent rotation of the heavens was due to the axial rotation of the Earth.

Datta — T. Hayashi A. Krishnaswamy Ayyangar — A. Singh — C. Rajagopal — T. Saraswati Amma — S. Sen — K. Shukla — K. Sarma — Babylon China Greece Islamic mathematics Europe. Indian astronomy. Devadas Gautama Siddha M. Babylonian astronomy Ancient Greek astronomy Hellenistic astronomy Islamic astronomy Chinese astronomy European astronomy.

Wikipedia aryabhatta contribution

The cause of rising and setting [is that] the sphere of the stars together with the planets [apparently? Aryabhata described a geocentric model of the Solar System, in which the Sun and Moon are each carried by epicycles. They in turn revolve around the Earth. The positions and periods of the planets was calculated relative to uniformly moving points.

In the case of Mercury and Venus, they move around the Earth at the same mean speed as the Sun. In the case of Mars, Jupiter, and Saturn, they move around the Earth at specific speeds, representing each planet's motion through the zodiac. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.

Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogony in which eclipses were caused by Rahu and Ketu identified as the pseudo-planetary lunar nodes , he explains eclipses in terms of shadows cast by and falling on Earth. Thus, the lunar eclipse occurs when the Moon enters into the Earth's shadow verse gola.

He discusses at length the size and extent of the Earth's shadow verses gola. Later Indian astronomers improved on the calculations, but Aryabhata's methods provided the core. His computational paradigm was so accurate that 18th-century scientist Guillaume Le Gentil , during a visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse of 30 August to be short by 41 seconds, whereas his charts by Tobias Mayer, were long by 68 seconds.

Considered in modern English units of time, Aryabhata calculated the sidereal rotation the rotation of the earth referencing the fixed stars as 23 hours, 56 minutes, and 4. Similarly, his value for the length of the sidereal year at days, 6 hours, 12 minutes, and 30 seconds As mentioned, Aryabhata advocated an astronomical model in which the Earth turns on its own axis.

Thus, it has been suggested that Aryabhata's calculations were based on an underlying heliocentric model, in which the planets orbit the Sun, [ 38 ] [ 39 ] [ 40 ] though this has been rebutted. Aryabhata's work was of great influence in the Indian astronomical tradition and influenced several neighbouring cultures through translations.

The Arabic translation during the Islamic Golden Age c. Some of his results are cited by Al-Khwarizmi and in the 10th century Al-Biruni stated that Aryabhata's followers believed that the Earth rotated on its axis. His definitions of sine jya , cosine kojya , versine utkrama-jya , and inverse sine otkram jya influenced the birth of trigonometry.

In fact, the modern terms "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misunderstood by Gerard of Cremona while translating an Arabic geometry text to Latin. He assumed that jiba was the Arabic word jaib , which means "fold in a garment", L.

Aryabhata's astronomical calculation methods were also very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world and used to compute many Arabic astronomical tables zijes. In particular, the astronomical tables in the work of the Arabic Spain scientist Al-Zarqali 11th century were translated into Latin as the Tables of Toledo 12th century and remained the most accurate ephemeris used in Europe for centuries.

Calendric calculations devised by Aryabhata and his followers have been in continuous use in India for the practical purposes of fixing the Panchangam the Hindu calendar. In the Islamic world, they formed the basis of the Jalali calendar introduced in CE by a group of astronomers including Omar Khayyam , [ 46 ] versions of which modified in are the national calendars in use in Iran and Afghanistan today.

The dates of the Jalali calendar are based on actual solar transit, as in Aryabhata and earlier Siddhanta calendars. This type of calendar requires an ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were less in the Jalali calendar than in the Gregorian calendar. Aryabhatta Knowledge University AKU , Patna has been established by Government of Bihar for the development and management of educational infrastructure related to technical, medical, management and allied professional education in his honour.

The university is governed by Bihar State University Act India's first satellite Aryabhata and the lunar crater Aryabhata are both named in his honour, the Aryabhata satellite also featured on the reverse of the Indian 2-rupee note. The inter-school Aryabhata Maths Competition is also named after him, [ 47 ] as is Bacillus aryabhata , a species of bacteria discovered in the stratosphere by ISRO scientists in Contents move to sidebar hide.

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