DiophantusDiophantus of Alexandria (born AD 200-214; died AD 284-298) was a Greek mathematician, who was the author of a series of books called Arithmetica, many of which are now lost. His texts deal with solving algebraic equations. Diophantine equations, Diophantine geometry, and Diophantine approximations are subareas of Number theory that are named after him. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality.
Āryabhaṭa's sine tableĀryabhata's sine table is a set of twenty-four numbers given in the astronomical treatise Āryabhatiya composed by the fifth century Indian mathematician and astronomer Āryabhata (476–550 CE), for the computation of the half-chords of a certain set of arcs of a circle. The set of numbers appears in verse 12 in Chapter 1 Dasagitika of Aryabhatiya. It is not a table in the modern sense of a mathematical table; that is, it is not a set of numbers arranged into rows and columns.
Chakravala methodThe chakravala method (चक्रवाल विधि) is a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation. It is commonly attributed to Bhāskara II, (c. 1114 – 1185 CE) although some attribute it to Jayadeva (c. 950 ~ 1000 CE). Jayadeva pointed out that Brahmagupta's approach to solving equations of this type could be generalized, and he then described this general method, which was later refined by Bhāskara II in his Bijaganita treatise.
KātyāyanaKātyāyana (कात्यायन) also spelled as Katyayana (est. 6th to 3rd century BCE) was a Sanskrit grammarian, mathematician and Vedic priest who lived in ancient India. According to some legends, he was born in the Katya lineage originating from Vishwamitra, thus called Katyayana. The Kathāsaritsāgara mentions Kātyāyana as another name of Vararuci, a re-incarnation of Lord Shiva's gana or follower Pushpadanta.
AryabhatiyaAryabhatiya (IAST: ) or Aryabhatiyam (), a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata. Philosopher of astronomy Roger Billard estimates that the book was composed around 510 CE based on historical references it mentions. Aryabhatiya is written in Sanskrit and divided into four sections; it covers a total of 121 verses describing different moralitus via a mnemonic writing style typical for such works in India (see definitions below): Gitikapada (13 verses): large units of time—kalpa, manvantara, and yuga—which present a cosmology different from earlier texts such as Lagadha's Vedanga Jyotisha (ca.
Brahmagupta's identityIn algebra, Brahmagupta's identity says that, for given , the product of two numbers of the form is itself a number of that form. In other words, the set of such numbers is closed under multiplication. Specifically: Both (1) and (2) can be verified by expanding each side of the equation. Also, (2) can be obtained from (1), or (1) from (2), by changing b to −b. This identity holds in both the ring of integers and the ring of rational numbers, and more generally in any commutative ring.
CombinationIn mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally, a k-combination of a set S is a subset of k distinct elements of S. So, two combinations are identical if and only if each combination has the same members.
Shulba SutrasThe Shulva Sutras or Śulbasūtras (Sanskrit: शुल्बसूत्र; : "string, cord, rope") are sutra texts belonging to the Śrauta ritual and containing geometry related to fire-altar construction. The Shulba Sutras are part of the larger corpus of texts called the Shrauta Sutras, considered to be appendices to the Vedas. They are the only sources of knowledge of Indian mathematics from the Vedic period. Unique fire-altar shapes were associated with unique gifts from the Gods.
Plimpton 322Plimpton 322 is a Babylonian clay tablet, notable as containing an example of Babylonian mathematics. It has number 322 in the G.A. Plimpton Collection at Columbia University. This tablet, believed to have been written about 1800 BC, has a table of four columns and 15 rows of numbers in the cuneiform script of the period. This table lists two of the three numbers in what are now called Pythagorean triples, i.e., integers a, b, and c satisfying a2 + b2 = c2.
AmoghavarshaAmoghavarsha I (also known as Amoghavarsha Nrupathunga I) (r.814–878 CE) was the greatest emperor of the Rashtrakuta dynasty, and one of the most notable rulers of Ancient India. His reign of 64 years is one of the longest precisely dated monarchical reigns on record. Many Kannada and Sanskrit scholars prospered during his rule, including the great Indian mathematician Mahaviracharya who wrote Ganita-sara-samgraha, Jinasena, Virasena, Shakatayan and Sri Vijaya (a Kannada language theorist).
