Both the form and the spirit of the arithmetic and algebra of modern times are essentially Indian. Think of our notation of numbers, brought to perfection by the Hindus, thinks of the arithmetical operations nearly as perfect as our own, think of their elegant algebraical methods, and then judge whether Brahmins on the banks of the Ganges are not entitled to some credit. Moreover, the ancient Indian algebra went far beyond the high school level.
The pinnacle of Indian achievement was attained in their solutions of the hard and subtle number — theoretic problems of finding integer solutions to equations of first and second degree. Such equations are called indeterminate or Diophantine equations.
But the sad part being, the Indian works in this branch were too far ahead of the times to be noticed by contemporary and subsequent civilisations!
Beside, developing the subject of algebra proper, Indians also began a process of algebraisation and consequent simplification of other area of mathematics. For Instance, they developed trigonometry in a systematic manner, resembling its modern form, and imparted to its modern algebraic character.
The algebraisation of the study of Infinitesimal changes led to the discovery of the key principles of Calculus at the time of Bhaskaracharya AD. Calculus in India reached astounding heights in the analytic trigonometry of the Kerala School in the 14 th century. Though the Greeks discovered trigonometry, their progress was halted due to absence of adequate algebraic machinery and notations.
Brahmagupta AD and Govindaswami AD gave interpolation formulae for calculating the sines of intermediate angles from sine tables- these are special cases of the Newton-Stirling and Newton-Gauss formulae for second — order difference.
The Greeks had investigated the relationship between a chord of a circle and the angle it subtends at the centre- but their system is quite cumbersome in practice. The Indians realized the significance of the connection between a half — chord and half of the angle subtended by the full chord. In the case of unit circle, this is precisely the sine function.
The Indian half- chord was introduced in the Arab world during the 8 th century AD. December 3, January 18, December 31, Uncategorized 0. Spread the love. Sharing is caring. This article is the 16th of a series on Muslim thinkers who greatly influenced Arab societies across the centuries. You can manage them any time by clicking on the notification icon. This section is about Living in UAE and essential information you cannot live without.
By clicking below to sign up, you're agreeing to our Terms of Use and Privacy Policy. Friday, November 12, All Sections. The common equation linear or quadratic was reduced in his book to one of six standard forms: 1. Squares equal to roots. Squares equal to numbers. Roots equal to numbers. Squares and roots equal to numbers. Squares and numbers equal to roots. Roots and numbers equal to squares. Insights on astronomy Al Khwarizmi wrote an important work on astronomy, covering calendars, calculation of true positions of the Sun, Moon and the planets, tables of sines and tangents, spherical astronomy, astrological tables and parallax and eclipse calculations, and focused on the visibility of the Moon.
Legacy to Arabs and Muslims While a good deal of controversy lingered on his major contributions — as to whether they were the result of original research or based on Hindu and Greek sources — few can deny that beyond his ability to synthesise existing knowledge that the Greeks, Indians and others assembled. List of works Al Khwarizmi was a prolific writer on Hindu-Arabic numerals.
More From Lifestyle. Do look down: Scaling one of NYC's tallest skyscrapers. Historically inspired watches from Seiko's range. Partner Content. Warning: You may not be able to drive a car after ! Indian and Chinese mathematicians recognised early on that one answer to this question was debts. For example, in a primitive farming context, if one farmer owes another farmer 7 cows, then effectively the first farmer has -7 cows.
If the first farmer goes out to buy some animals to repay his debt, he has to buy 7 cows and give them to the second farmer in order to bring his cow tally back to 0. From then on, every cow he buys goes to his positive total. This reluctance to adopt negative numbers, and indeed zero, held European mathematics back for many years. Gottfried Wilhelm Leibniz was one of the first Europeans to use zero and the negatives in a systematic way in his development of calculus in the late 17th century.
Calculus is used to measure rates of changes and is important in almost every branch of science, notably underpinning many key discoveries in modern physics. The Kerala school of astronomy and mathematics , founded by Madhava of Sangamagrama in the s, was responsible for many firsts in mathematics, including the use of mathematical induction and some early calculus-related results. Although no systematic rules for calculus were developed by the Kerala school, its proponents first conceived of many of the results that would later be repeated in Europe including Taylor series expansions, infinitessimals and differentiation.
The leap, made in India, that transformed zero from a simple placeholder to a number in its own right indicates the mathematically enlightened culture that was flourishing on the subcontinent at a time when Europe was stuck in the dark ages. Although its reputation suffers from the Eurocentric bias , the subcontinent has a strong mathematical heritage, which it continues into the 21st century by providing key players at the forefront of every branch of mathematics.
0コメント