Aryabhata - The Inventor of Zero (0)

Aryabhatta

Aryabhatta

Name For Ancient Indian Mathematics and Astronomical Development 

Aryabhata (आर्यभट) was a Bharatiya mathematician and astronomer of the classical age of Bharatiya Mathematics and Astronomy. He was born in 476 CE in Kusumapura (Pataliputra), Gupta Empire (modern-day Patna ,Bharat{India}) to and decreased in 550 CE in Pataliputra . He produced works such as  Āryabhaṭīyam आर्यभटीयम् and Arya-siddhanta आर्य-सिद्धांत .

Aryabhata created a system of phonemic number notation in which numbers were represented by consonant-vowel monosyllables .Later commentators divided his work into गणित  Mathematics,कालक्रिया Calculations on Time and गोलपाड़ा Spherical Astronomy.

Mathematics

He is Best known for his invention of Zero (in his Place value System).

He gave the approximation value of π(pi) {as irrational number}.In the second part of  the Aryabhatiyam (gaṇitapāda 10), आर्यभटीयम्  (गणितपाद 10) he writes:

चतुराधिकं शतमष्टगुणं द्वाषष्टिस्तथा सहस्राणाम्।

अयुतद्वयस्य विष्कम्भस्यासन्नो वृत्तपरिणाहः॥

"Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."

his implies that for a circle whose diameter is 20000, the circumference will be 62832

i.e., ${\displaystyle \pi }$ = ${\displaystyle 62832 \over 20000}$ = ${\displaystyle 3.1416}$ , which is accurate to three  decimal places.

In trigonometry ,

He was the first to specify sine and versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.The first use of the idea of ‘sine’ in the way we use it today was in the work Aryabhatiyamआर्यभटीयम् by Aryabhata, in A.D. 500. Aryabhata used the word ardha-jya अर्ध-ज्या for the half-chord, which was shortened to jya  ज्या or jiva जीवा in due course. When the Aryabhatiyam was translated into Arabic, the word jiva जीवा was retained as it is. The word jiva जीवा was translated into sinus, which means curve, when the Arabic version was translated into Latin. Soon the word sinus, also used as sine, became common in mathematical texts throughout Europe.

Indeterminate equations

He also worked on equations which have one or more unknown variables(known as Diophantine Equation).

Here is an example from Bhāskara(भास्कर)'s commentary on Aryabhatiya:

Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7

That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85. In general, diophantine equations, such as this, can be notoriously difficult. Aryabhata's method of solving such problems, elaborated by Bhaskara in 621 CE, is called the kuṭṭaka (कुट्टक) method{कुट्टक means break into small pieces}. the method involves a recursive algorithm for writing the original factors in smaller numbers. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, and initially the whole subject of algebra was called kuṭṭaka-gaṇita कुट्टक-गणित or simply kuṭṭaka कुट्टक  .

Algebra

In Aryabhatiya, Aryabhata provided elegant results for the summation of series of squares and cubes:

${\displaystyle 1^{2}+2^{2}+\cdots +n^{2}={n(n+1)(2n+1) \over 6}}$

and

${\displaystyle 1^{3}+2^{3}+\cdots +n^{3}=(1+2+\cdots +n)^{2}}$

Astronomy

Aryabhata actually was at that level in Astronomy (in that time) that he knew about the facts which the so-called "Modern Astronomy" of the West has proved now. 

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. 820 CE), was particularly influential. 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. 

Aryabhata's system of astronomy was called the audAyaka system औदायक प्रणाली , in which days were reckoned माना from Dawn (Sunrise) उदय at Lanka 

Aryabhatta discovered world is round, rotates on axis much before Copernicus

Aryabhata correctly insisted that the earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the earth, contrary to the then-prevailing view, that the sky rotated. <This is indicated in the first chapter of Aryabhatika>

He also Explained Cosmic Winds

In the same way that someone in a boat going forward sees an unmoving [object] going backward, so [someone] on the equator sees the unmoving stars going uniformly westward. The cause of rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at the equator, constantly pushed by the cosmic wind.

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. In this model, which is also found in the Paitāmahasiddhāntaपैतामहसिद्धान्त(c. CE 425), the motions of the planets are each governed by two epicycles, a smaller mandaमंद (slow) and a larger śīghra शीघ्र (fast). The order of the planets in terms of distance from earth is taken as: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms

Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon and planets shine by reflected sunlight.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.37). He discusses at length the size and extent of the Earth's shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. 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 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds, which means Hundreds years old Indian computations (by his Method) were far more accurate than that of European Computation of that time.

Aryabhata calculated the rotation of the earth referencing the fixed stars as 23 hours, 56 minutes, and 4.1 seconds (Modern calculation is 23:56:4.091)

Aryabhata calculated  time taken by the Earth to orbit the Sun once with respect to the fixed stars as 365.25858 days (Modern caculation is 365.25636 days)[a difference of 3 minutes and 20 seconds]

Calendric calculations devised by Aryabhata and his followers have been in continuous use in India for the practical purposes of fixing the Panchangam पंचांग.  In the Islamic world, they formed the basis of the Jalali calendar. 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.

Honours Given to him in Independent India

• Government of Bihar established a University named after him Aryabhatta Knowledge University (AKU), Patna.
• India's first Satellite was named as Aryabhata 
• India's first Lunar crater was named as Aryabhata
•  An Institute for conducting research in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institute of Observational Sciences (ARIES) near Nainital, India.
• The inter-school Aryabhatta Maths Competition is also named after him
• Bacillus aryabhata, a species of bacteria discovered in the stratosphere by ISRO scientists in 2009 

You can also learn about these from below:

Aryabhatta Knowledge University (AKU)

Aryabhata Satellite

Aryabhata Crater

Aryabhatta Research Institute of Observational Sciences (ARIES)

The inter-school Aryabhatta Maths Competition

Bacillus aryabhata