 | Indian mathematics: Encyclopedia II - Indian mathematics - Vedic Mathematics 1500 BC - 500 BC
Indian mathematics - Vedic Mathematics 1500 BC - 500 BC
As a result of the mathematics required for the construction of religious altars, many rules and developments of geometry are found in Vedic works, along with many astronomical developments for religious purposes. These include the use of geometric shapes, including triangles, rectangles, squares, trapezia and circles, equivalence through numbers and area, squaring the circle and visa-versa, the Pythagorean theorem and Pythagorean triples, and computations of π.
Vedic works also contain all four arithmetical operators (addition, subtraction, multiplication and division), a definite system for denoting any number up to 1055, the existence of zero, prime numbers, the rule of three, and a number of other discoveries. Of all the mathematics contained in the Vedic works, it is the definite appearance of decimal symbols for numerals and a place value system that should perhaps be considered the most phenomenal.
Indian mathematics - Vedas 1500 BC - 500 BC
The Rig-Veda contains rules for the construction of great fire altars.
The Yajur Veda contains the earliest known use of numbers up to a trillion (parardha). It even discusses the concept of numeric infinity (purna "fullness"), stating that if you subtract purna from purna, you are still left with purna.
Arithmetical sequences are found in the Atharva-Veda.
Indian mathematics - Samhitas 1500 BC - 500 BC
The Samhitas contain fractions, aswell as equations, such as 972x2 = 972 + m for example, along with rules implying knowledge of the Pythagorean theorem.
The Taittiriya Samhita contains rules for the construction of great fire altars, and gives a rule implying knowledge of the Pythagorean theorem.
Indian mathematics - Lagadha 1350 BC - 800 BC
Lagadha composed the Vedanga Jyotisha, which describes rules for tracking the motions of the sun and the moon. Lagadha is the only known mathematician to have used geometry and trigonometry for astronomy, much of whose works were destroyed by foreign invaders of India.
Indian mathematics - Yajnavalkya 1000 BC - 600 BC
Yajnavalkya composed the Shatapatha Brahmana, which contains geometric, constructional, algebraic and computational aspects. It contains several computations of π, with the closest being correct to 2 decimal places (the most accurate value of π upto that time), and gives a rule implying knowledge of the Pythagorean theorem, while the work also contains references to the motions of the sun and the moon. Yajnavalkya also advanced a 95-year cycle to synchronize the motions of the sun and the moon.
Indian mathematics - Sulba Sutras 800 BC - 500 BC
Sulba Sutra means "Rule of Chords" in Vedic Sanskrit, which were appendices to the Vedas giving rules for the construction of religious altars. The Sulba Sutras contain the first use of irrational numbers, quadratic equations of the form a x2 = c and ax2 + bx = c, unarguable evidence for the use of the Pythagorean theorem and Pythagorean triples predating Pythagoras (572 BC - 497 BC), and evidence of a number of geometrical proofs. These discoveries are mostly a result of altar construction, which also led to the first known calculations for the square root of 2 found in three of the Sulba Sutras, which were remarkably accurate.
Baudhayana composed the Baudhayana Sulba Sutra, which contains the Pythagorean theorem, geometric solutions of a linear equation in a single unknown, several approximations of π (the closest value being 3.114), along with the first use of irrational numbers and quadratic equations of the forms ax2 = c and ax2 + bx = c, and the first known calculation for the square root of 2, which was correct to a remarkable five decimal places.
Manava composed the Manava Sulba Sutra, which contains approximate constructions of circles from rectangles, and squares from circles, which give approximate values of π, with the closest value being 3.125.
Apastamba composed the Apastamba Sulba Sutra, which makes an attempt at squaring the circle and also considers the problem of dividing a segment into 7 equal parts. It also calculates the square root of 2 correct to five decimal places, and solves the general linear equation. The Apastamba Sulba Sutra also contains a numerical proof of the Pythagorean theorem, using an area computation. According to Albert Burk, this is the original proof of the theorem, and Pythagoras copied it. Many scholars find Burk's claim unsubstantiated however.
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