**Pingala** (**पिङ्गल** *piṅgalá*) is the supposed author of the **Chandas shastra** (*chandaḥ-śāstra*, also Chandas sutra *chandaḥ-sūtra*), a Sanskrit treatise on prosody considered one of the Vedanga. The verses of the Vedas have a variety of different meters. ...
Shastra is a Sanskrit word used to denote education/knowledge in a general sense. ...
Sanskrit ( à¤¸à¤‚à¤¸à¥à¤•à¥ƒà¤¤à¤®à¥ ; pronunciation: ) is an Indo-European classical language of India and a liturgical language of Hinduism, Buddhism, and Jainism. ...
Prosody may mean several things: Prosody consists of distinctive variations of stress, tone, and timing in spoken language. ...
The Vedanga (IAST , member of the Veda) are six auxiliary disciplines for the understanding and tradition of the Vedas. ...
In Indian literary tradition, Pingala is identified as the younger brother of Panini, the great grammarian of ca. 5th century BC. Other traditions identify him with Patanjali, the author of the Mahabhashya. The title given to this article is incorrect due to technical limitations. ...
Patañjali, is the compiler of the Yoga Sutra, a major work containing aphorisms on the practical and philosophical wisdom regarding practice of Raja yoga. ...
The MahÄbhÄá¹£ya (great commentary), attributed to PataÃ±jali, is a commentary on the celebrated Ashtadhyayi of Panini is one of the three most famous works in Sanskrit grammar. ...
Mylius (1983:68) considers the Chandas-shastra as "very late" within the Vedanga corpus. This would place it close to the beginning of the Common Era, likely post-dating Mauryan times. The Common Era (CE), sometimes known as the Christian Era or Current Era, is the period of measured time beginning with the year 1 (the traditional birthdate of Jesus) to the present. ...
The Mauryan empire (321 to 185 BCE), at its largest extent around 230 BCE. The Mauryan empire was Indias first great unified empire. ...
The shastra is divided into eight chapters. It was edited by Weber (1863). It is at the transition between Vedic meter and the classical meter of the Sanskrit epics. The 10th century mathematician Halayudha commented and expanded it. Pingala presents the first known description of a binary numeral system. He described the binary numeral system in connection with the listing of Vedic meters with short and long syllables. His discussion of the combinatorics of meter, corresponds to the binomial theorem. Halayudha' s commentary includes a presentation of the Pascal's triangle (called *meru-prastaara*). Pingala's work also contains the basic ideas of Fibonacci number (called *maatraameru* ). The verses of the Vedas have a variety of different meters. ...
Halayudha (à¤¹à¤²à¤¾à¤¯à¥à¤§) was a 10th century Indian mathematician, wrote a commentary on Pingalas Chandah-shastra where Pingalas knowledge of the meru-prastaara (Pascals triangle) is explicitly mentioned. ...
The binary numeral system (base 2 numerals) represents numeric values using two symbols, typically 0 and 1. ...
In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. ...
1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 The first six rows of Pascals triangle In mathematics, Pascals triangle is a geometric arrangement of the binomial coefficients in a triangle. ...
Mount Meru is a sacred mountain in Hindu mythology which is believed to be the abode of Brahma and other gods. ...
In mathematics, the Fibonacci numbers, named after Leonardo of Pisa, known as Fibonacci, form a sequence defined recursively by: In other words, each number is the sum of the two numbers before it. ...
Use of zero is sometimes mistakenly ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion, while Pingala used short and long syllables. Four short syllables (binary "0000") in Pingala's system, however, represented the number one, not zero. Positional use of zero dates from later centuries and would have been known to Halayudha but not to Pingala. 0 (zero) is both a number and a numeral. ...
Halayudha (à¤¹à¤²à¤¾à¤¯à¥à¤§) was a 10th century Indian mathematician, wrote a commentary on Pingalas Chandah-shastra where Pingalas knowledge of the meru-prastaara (Pascals triangle) is explicitly mentioned. ...
## Editions
- A. Weber,
*Indische Studien* 8, Leipzig, 1863. - Bibliotheca Indica, Calcutta 1871-1874, reprint 1987.
Albrecht Weber (born 17 February 1825 in Breslau; died 30 November 1901) was a German indologist and historian. ...
## References - George Gheverghese Joseph.
*The Crest of the Peacock: Non-European Roots of Mathematics*, Penguin Books, 2000. - Klaus Mylius,
*Geschichte der altindischen Literatur*, Wiesbaden (1983). Penguin Books is a British publisher founded in 1935 by Allen Lane. ...
## See also The verses of the Vedas have a variety of different meters. ...
The chronology of Indian mathematics spans from the Indus Valley civilization (3300-1500 BC) and Vedic civilization (1500-500 BC) to modern India (21st century AD). ...
Here is a chronology of the main Indian mathematicians: BC Yajnavalkya, 1800 BC, the author of the altar mathematics of the Shatapatha Brahmana. ...
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