Varāhamihira

Varāhamihira (505–587 CE), also called Varaha or Mihir, was an Indian astronomer, mathematician, and astrologer who lived in Ujjain. He was born in Avanti (India) region, roughly corresponding to modern-day Malwa, to Adityadasa, who was himself an astronomer. According to one of his own works, he was educated at Kapitthaka. He is considered to be one of the "Nine Jewels" (Navaratnas) of the court of legendary ruler Yashodharman Vikramaditya of Malwa.

Works

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Pancha-Siddhantika

Varahamitra'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 Siddhanta. It is a compendium of Vedanga Jyotisha as well as Hellenistic astronomy(including Greek, Egyptian and Roman elements).Varahamihira was the first one to mention that the ayanamsa, or the shifting of the equinox is 50.32 seconds.

"They [the Indians] have 5 Siddhāntas:

• Sūrya-Siddhānta, ie. the Siddhānta of the Sun, thought to be composed by Lāṭadeva,but actually composed by Mayasuraalso known as Mamuni Mayan as stated in the text itself.
• Vasishtha-siddhānta, so called from one of the stars of the Great Bear, composed by Vishnucandra,
• Paulisa-siddhānta, so called from Pulisa, the Greek, from the city of Saintra, which is supposed to be Alexandria, composed by Pulisa.
• Romaka-siddhānta, so called from the Rūm, ie. the subjects of the Roman Empire, composed by Śrīsheṇa.
• Paitahama-siddhānta.

Brihat-Samhita

Another important contribution of Varahamihira is the encyclopedic Brihat-Samhita. It covers wide ranging subjects of human interest, including astrology, planetary movements, eclipses, rainfall, clouds, architecture, growth of crops, manufacture of perfume, matrimony, domestic relations, gems, pearls, and rituals. The volume expounds on gemstone evaluation criterion found in the Garuda Purana, and elaborates on the sacred Nine Pearls from the same text. It contains 106 chapters and is known as the "great compilation".

On Astrology

He was also an astrologer. He wrote on all the three main branches of Jyotisha astrology:

• Brihat Jataka - is considered as one of the five main treatises on Hindu astrology on horoscopy.
• Laghu Jataka - also known as 'Swalpa Jataka'
• Samasa Samhita - also known as 'Lagu Samhita' or 'Swalpa Samhita'
• Brihat Yogayatra - also known as 'Mahayatra' or 'Yakshaswamedhiya yatra'
• Yoga Yatra - also known as 'Swalpa yatra'
• Tikkani Yatra
• Brihat Vivaha Patal
• Lagu Vivaha Patal - also known as 'Swalpa Vivaha Patal'
• Lagna Varahi
• Kutuhala Manjari
• Daivajna Vallabha (apocryphal)

His son Prithuyasas also contributed to Hindu astrology; his book Hora Sara is a famous book on horoscopy. Khana (also named Lilavati elsewhere), the medieval Bengali poet astrologer, is believed to be the daughter-in-law of Varahamihira.

Sankhya-Siddhanta

Another of Varahamihira's lesser known works is the Sankhya-Siddhanta. Not much is known about this work, since only a fragment of it was recovered. From what has been recovered, archaeologists state that it dealt with advanced arithmetic, trigonometry, as well as some relatively basic concepts.^{[citation needed]}

Influences

The Romaka Siddhanta ("Doctrine of the Romans") and the Paulisa Siddhanta ("Doctrine of Paul") were two works of Western origin which influenced Varahamihira's thought, though this view is controversial as there is much evidence to suggest that it was actually Vedic thought indigenous to India which first influenced Western astrologers and subsequently came back to India reformulated. Number of his writings share similarities with the earlier texts like Vedanga Jyotisha.

A comment in the Brihat-Samhita by Varahamihira says: "The Greeks, though barbarians.,must be honored since they have shown tremendous interest in our science....." 

Contributions

Trigonometry

Varahamihira's mathematical work included the discovery of the trigonometric formulas

${\displaystyle \sin ^{2}x+\cos ^{2}x=1\;\!}$

${\displaystyle \sin x=\cos \left({\frac {\pi }{2}}-x\right)}$

${\displaystyle {\frac {1-\cos 2x}{2}}=\sin ^{2}x}$

Varahamihira improved the accuracy of the sine tables of Aryabhata .

Arithmetic

He defined the algebraic properties of zero as well as of negative numbers.

Combinatorics

He was among the first mathematicians to discover a version of what is now known as the Pascal's triangle. He used it to calculate the binomial coefficients.