Pingala
Pingala (Devanagari: पिङ्गल piṅgala) is the traditional name of the author of the Chandaḥśāstra (also Chandaḥsūtra), the earliest known Sanskrit treatise on prosody.
The Chandaḥśāstra presents the first known description of a
binary numeral system in connection with the systematic enumeration of meters with fixed patterns of short and long syllables.[4] The discussion of the combinatorics of meter corresponds to the binomial theorem. Halāyudha's commentary includes a presentation of the Pascal's triangle (called meruprastāra). Pingala's work also contains the Fibonacci number, called mātrāmeru, and now known as the Gopala–Hemachandra number.[5]
Varāhamihira
Varāhamihira pronunciation (help·info) (Devanagari: वराहमिहिर
(505–587 CE), also called Varaha or Mihir, was an Indian astronomer, mathematician, and astrologer who lived in Ujjain.He was Shrigaud Brahmin.[1] He is considered to be one of the nine jewels (Navaratnas) of the court of legendary ruler Vikramaditya (thought to be the Gupta emperor Chandragupta II Vikramaditya).
arahamihir's main work is the book Pañcasiddhāntikā (or Pancha-Siddhantika, "[Treatise] on the Five [Astronomical] Canons) dated ca. 575 CE gives us information about older Indian texts which are now lost. The work is a treatise on mathematical astronomy and it summarises five earlier astronomical treatises, namely the Surya Siddhanta, Romaka Siddhanta, Paulisa Siddhanta, Vasishtha Siddhanta and Paitamaha Siddhantas. It is a compendium of Vedanga Jyotisha as well as Hellenistic astronomy (including Greek, Egyptian and Roman elements).[2] He was the first one to mention in his work Pancha Siddhantika that the ayanamsa, or the
shifting of the equinox is 50.32 seconds.6655.
Bhāskara I
Bhāskara (c. 600 – c. 680) (Marathi: भास्कर commonly called Bhaskara I to avoid confusion with the 12th century mathematician Bhāskara II) was a 7th century Indian mathematician, who was apparently the first to write numbers in the
Hindu-Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work.[1] This commentary, Āryabhaṭīyabhāṣya, written in 629 CE, is the oldest known prose work in Sanskrit on mathematics and astronomy. He also wrote two astronomical works in the line of Aryabhata's school, the Mahābhāskarīya and the Laghubhāskarīya.[2]
Brahmagupta
Brahmagupta (Sanskrit: ब्रह्मगुप्त; listen (help·info)) (597–668 AD) was a great Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta (Correctly Established Doctrine of Brahma), written in 628 in Bhinmal. Its 25 chapters contain several unprecedented mathematical results.
Brahmagupta was the first to use zero as a number. He gave rules to compute with zero. Brahmagupta used negative numbers and zero for computing. The modern rule that two negative numbers multiplied together equals a positive number first appears in Brahmasputa siddhanta. It is composed in elliptic verse, as was common practice in Indian mathematics, and consequently has a poetic ring to it. As no proofs are given, it is not known how Brahmagupta's mathematics was derived.[1]
Mahāvīra
Mahavira was a 9th-century Indian mathematician from Gulbarga who asserted that the square root of a negative number did not exist. He gave the sum of a series whose terms are squares of an arithmetical progression and empirical rules for area and perimeter of an ellipse. He was patronised by the great Rashtrakuta king Amoghavarsha.[1]
Mahavira was the author of Ganit Saar Sangraha. He separated Astrology from Mathematics. He expounded on the same subjects on which Aryabhata and Brahmagupta contended, but he expressed them more clearly. He is highly respected among Indian Mathematicians, because of his establishment of terminology for concepts such as equilateral, and isosceles triangle; rhombus; circle and semicircle. Mahavira's eminence spread in all South India and his books proved inspirational to other Mathematicians in Southern India.[2] It was translated into Telugu language by Pavuluri Mallana as Saar Sangraha Ganitam.
Acharya Hemachandra
Acharya Hemachandra (Sanskrit: हेमचन्द्र सूरी, 1087–1172) was a Jain scholar, poet, and polymath who wrote on grammar, philosophy, prosody, and contemporary history. Noted as a prodigy by his contemporaries, he gained the title Kalikāl Sarvagya "all-knowing of the Kali Yuga".
He was born in Dhandhuka, Gujarat (about 100 km south west of Ahmadabad), to Chachadeva and Pahini Devi. They named him Chandradeva. The Jain derasar of Modhera Tirtha is located at his birthplace. As a young man, Chandradeva was initiated as a monk at a derasar and took the name Somachandra. He was trained in religious discourse, philosophy, logic and grammar. In 1110, at the age of 21, he was ordained as an acharya of the Svetambara sect of Jainism and was given the name Somachandra (popularly Hemachandra).[1]
Mahendra Sūri
Mahendra Dayashankar Gor Sūri is the 14th century Jain astronomer who wrote the Yantraraja, the first Indian treatise on the astrolabe.[1] He was a pupil of Madana Suri. His father was Dayashankar and mother was Vimla. Dayashankar and Vimla had eight children, four sons and four daughters. Mahendra married a woman by the name of Urmila and had four daughters.
Madhava of Sangamagrama
Madhava of Sangamagrama (Malayalam: സംഗമഗ്രാമ മാധവൻ, Saṅgamagrāma Mādhavan ?, Hindi: संगमग्राम के माधव, Saṅgamagrāma kē Mādhava ?; c. 1340 – c. 1425), was an Indian mathematician-astronomer from the town of Sangamagrama (present day Irinjalakuda) near Cochin, Kerala, India. He is considered the founder of the Kerala school of astronomy and mathematics. He was the first in the world to use infinite series approximations for a range of trigonometric functions, which has been called the "decisive step onward from the finite procedures of ancient mathematics to treat their limit-passage to infinity".[1]
His discoveries opened the doors to what has today come to be known as Mathematical Analysis.[4] One of the greatest mathematician-astronomers of the Middle Ages, Madhava made pioneering contributions to the study of infinite series, calculus, trigonometry, geometry, and algebra.
Some scholars have also suggested that Madhava's work, through the writings of the Kerala school, may have been transmitted to Europe via Jesuit missionaries and traders who were active around the ancient port of Muziris at the time.
As a result, it may have had an influence on later European developments in analysis and calculus.[5]
Parameshvara
Vatasseri Parameshvara Nambudiri (Malayalam: വടശ്ശേരി പരമേശ്വരന്*) (ca.1380–1460)[1] was a major Indian mathematician and astronomer of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama. He was also an astrologer. Parameshvara was a proponent of observational astronomy in medieval India and he himself had made a series of eclipse observations to verify the accuracy of the computational methods then in use. Based on his eclipse observations, Parameshvara proposed several corrections to the astronomical parameters which had been in use since the times of Aryabhata. The computational scheme based on the revised set of parameters has come to be known as the Drgganita system. Parameshvara was also a prolific writer on matters relating to astronomy. At least 25 manuscripts have been identified as being authored by Parameshvara.[1]
Parameshvara's most significant contribution is his mean value type formula for the inverse interpolation of the sine. He was the first mathematician to give the radius of circle with an inscribed quadrilateral, an expression that is normally attributed to Lhuilier (1782), 350 years later. With the sides of the cyclic quadrilateral being a, b, c, and d, the radius R of the circumscribed circle is:
Nilakantha Somayaji
Kelallur Nilakantha Somayaji (Malayalam: നീലകണ്ഠ സോമയാജി, Nīlakaṇṭa Sōmayāji ?, Sanskrit: नीलकण्ठ सोमयाजि
(1444–1544) (also referred to as Kelallur Comatiri[1]) was a major mathematician and astronomer of the Kerala school of astronomy and mathematics. One of his most influential works was the comprehensive astronomical treatise Tantrasamgraha completed in 1501. He had also composed an elaborate commentary on Aryabhatiya called the Aryabhatiya Bhasya. In this Bhasya, Nilakantha had discussed infinite series expansions of trigonometric functions and problems of algebra and spherical geometry. Grahapareeksakrama is a manual on making observations in astronomy based on instruments of the time.
Regarding Arya Batta and Bhaskara2 I have mentioned in my earlier posts.
