Brahmagupta

Brahmagupta was a seventh-century Indian mathematician and astronomer whose works systematized arithmetic, algebra, and mathematical astronomy. His rules for zero and negative numbers and formula for cyclic quadrilaterals became enduring contributions.

Brahmasphutasiddhanta: Brahmagupta’s Sanskrit treatise on astronomy and mathematics, completed in 628 CE. This work contains his best-known treatments of arithmetic, algebra, and planetary calculations.
Brahmagupta's formula: A formula for the area of a cyclic quadrilateral in terms of its four side lengths. It is his most celebrated geometric result and extends Heron’s triangle-area formula.
Muhammad al-Fazari: An eighth-century scholar associated with translating Indian astronomical material into Arabic. The Arabic reception of Indian astronomy helped carry traditions represented by Brahmagupta’s work westward.
Aryabhata's astronomy: The astronomical system presented by Aryabhata, including mathematical models for celestial motions. Brahmagupta challenged several of Aryabhata’s astronomical explanations and computational choices.
Indian numeral system: The place-value numeral system developed in India, including the use of zero as a number. Its positional notation underlies the arithmetic rules Brahmagupta set out.
Zero: A number representing none, also used as a placeholder in positional notation. Brahmagupta stated arithmetic rules involving zero, including its interaction with positive and negative numbers.
Al-Khwarizmi: A ninth-century mathematician whose works shaped algebra and the transmission of Hindu-Arabic numerals. His arithmetic and astronomical writings reflect the broader Arabic adoption of Indian mathematical knowledge.
Ptolemaic astronomy: An ancient geocentric system that models celestial motions using deferents and epicycles. It offers a major non-Indian comparison for the mathematical astronomy Brahmagupta practiced.
Sanskrit mathematics: Mathematical knowledge composed and transmitted in Sanskrit across South Asia. Brahmagupta wrote within this scholarly tradition, using compact verse to state procedures.
Negative number: A number less than zero, representing a quantity below a chosen reference point. His arithmetic treated positive and negative quantities as fortunes and debts.

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