Halāyudha (
Sanskrit
Sanskrit (; stem form ; nominal singular , ,) is a classical language belonging to the Indo-Aryan languages, Indo-Aryan branch of the Indo-European languages. It arose in northwest South Asia after its predecessor languages had Trans-cultural ...
: हलायुध) wrote the ', a
commentary on
Pingala
Acharya Pingala (; c. 3rd2nd century BCE) was an ancient Indian poet and mathematician, and the author of the ' (), also called the ''Pingala-sutras'' (), the earliest known treatise on Sanskrit prosody.
The ' is a work of eight chapters in the ...
's ''Chandaḥśāstra'', was an Indian Mathematician and poet who lived and worked in the 10th century. The ''
Chandaḥśāstra'' by the Indian lyricist
Piṅgala (3rd or 2nd century BC) somewhat crypically describes a method of arranging two types of syllables to form
metre
The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...
s of various lengths and counting them; as interpreted and elaborated by
Halāyudha his "method of pyramidal expansion" (''meru-prastāra'') for counting metres is equivalent to
Pascal's triangle
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Bla ...
.
Biography
Halayudha originally resided at the
Rashtrakuta
The Rashtrakuta Empire was a royal Indian polity ruling large parts of the Indian subcontinent between the 6th and 10th centuries. The earliest known Rashtrakuta inscription is a 7th-century copper plate grant detailing their rule from Manapu ...
capital
Manyakheta, where he wrote under the patronage of emperor
Krishna III
Krishna III (r. 939 – 967), whose Kannada name was Kannara, was the last great warrior and able Rashtrakuta Emperor. He was a shrewd administrator and skillful military campaigner. He waged many wars to restore the glory of the Rashtrakuta ...
. His ''Kavi-Rahasya'' eulogizes Krishna III. Later, he migrated to
Ujjain
Ujjain (, , old name Avantika, ) or Ujjayinī is a city in Ujjain district of the Indian state of Madhya Pradesh. It is the fifth-largest city in Madhya Pradesh by population and is the administrative as well as religious centre of Ujjain ...
in the
Paramara kingdom. There, he composed ''Mṛta-Sañjīvanī'' in honour of the Paramara king
Munja.
Works
Halayudha composed the following works:
* ''Kavi-Rahasya'', a book on poetics
* ''Mṛta-Sañjīvanī'', a commentary on Pingala's ''Chandaḥ-śāstra''
* ''Abhidhana-ratna-mala'', a lexicon
* ''Halāyudha Kośa'', a dictionary
See also
*
Indian mathematicians
Indian mathematicians have made a number of contributions to mathematics that have significantly influenced scientists and mathematicians in the modern era. One of such works is Hindu numeral system which is predominantly used today and is likely ...
References
Bibliography
History of Rashtrakutas
*
10th-century Indian mathematicians
Indian Sanskrit scholars
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