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Varāhamihira
वराहमिहिर Varāhamihira  

Born  505 CE 
Died  587 CE 
Occupation  astronomer, mathematician, and astrologer 
Nationality  Indian 
Ethnicity  Indian 
Period  Gupta era 
Subject  Astronomy, Astrology, Mathematics 
Notable works  PanchaSiddhāntikā, BrihatSamhita, Brihat Jataka 
Varāhamihira About this sound 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 born in Avanti region, roughly corresponding to modernday Malwa, to Adityadasa, who was himself an astronomer. According to one of his own works, he was educated at Kapitthaka.^{[1]} He is considered to be one of the nine jewels (Navaratnas) of the court of legendary ruler Yashodharman Vikramaditya of Malwa.^{[2]}^{[3]}
Contents
Works
He was the first one to mention in his work Pañcasiddhāntikā that the ayanamsa, or the shifting of the equinox, is 50.32 seconds.
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PanchaSiddhantika
Varahamihira's main work is the book Pañcasiddhāntikā (or PanchaSiddhantika, "[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).^{[4]} 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.
The 11th century Iranian scholar Alberuni also described the details of "The Five Astronomical Canons":
 "They [the Indians] have 5 Siddhāntas:
 SūryaSiddhānta, ie. the Siddhānta of the Sun, thought to be composed by Lāṭadeva,but actually composed by Mayasura also known as Mamuni Mayan as stated in the text itself.
 Vasishthasiddhānta, so called from one of the stars of the Great Bear, composed by Vishnucandra,
 Paulisasiddhānta, so called from Pulisa, the Greek, from the city of Saintra, which is supposed to be Alexandria, composed by Pulisa.
 Romakasiddhānta, so called from the Rūm, ie. the subjects of the Roman Empire, composed by Śrīsheṇa.
 Paitahamasiddhānta.
BrihatSamhita
Another important contribution of Varahamihira is the encyclopedic BrihatSamhita. 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 in the Hindu astrology; his book Hora Sara is a famous book on horoscopy. Khana (also named Lilavati elsewhere) the medieval Bengali poetess astrologer is believed to be the daughterinlaw of Varahamihir.
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.^{[5]} Number of his writings share similarities with the earlier texts like Vedanga Jyotisha.^{[6]}
A comment in the BrihatSamhita by Varahamihira says: "The Greeks, though barbarians.,^{[7]} must be honored since they have shown tremendous interest in our science....." ("mleccha hi yavanah tesu samyak shastram kdamsthitam/ rsivat te 'p i pujyante kim punar daivavid dvijah" (BrihatSamhita 2.15)).
Contributions
Trigonometry
Varahamihira's mathematical work included the discovery of the trigonometric formulas
 <math> \sin^2 x + \cos^2 x = 1 \;\!</math>
 <math> \sin x = \cos\left(\frac{\pi} {2}  x \right) </math>
 <math> \frac {1  \cos 2x}{2} = \sin^2x </math>
Varahamihira improved the accuracy of the sine tables of Aryabhata I.
Arithmetic
He defined the algebraic properties of zero as well as of negative numbers.^{[8]}
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.^{[9]}^{[10]}^{[11]}
Optics
Among Varahamihira's contribution to physics is his statement that reflection is caused by the backscattering of particles and refraction (the change of direction of a light ray as it moves from one medium into another) by the ability of the particles to penetrate inner spaces of the material, much like fluids that move through porous objects.^{[12]}
1. ^ "the Pañcasiddhāntikā ("Five Treatises"), a compendium of Greek, Egyptian, Roman and Indian astronomy. Varāhamihira's knowledge of Western astronomy was thorough. In 5 sections, his monumental work progresses through native Indian astronomy and culminates in 2 treatises on Western astronomy, showing calculations based on Greek and Alexandrian reckoning and even giving complete Ptolemaic mathematical charts and tables. Encyclopædia Britannica (2007) s.v.Varahamihira ^
2. E. C. Sachau, Alberuni's India (1910), vol. I, p. 153
See also
Notes
 ^ J J O'Connor & E F Robertson. "Varahamihira".
 ^ History of Indian Literature. Motilal Banarsidass Publications. 2008. p. 46.
 ^ Ram Gopal (1984). Kālidāsa: His Art and Culture. Concept Publishing Company. p. 15.
 ^ "the Pañcasiddhāntikā ("Five Treatises"), a compendium of Greek, Egyptian, Roman and Indian astronomy. Varāhamihira's knowledge of Western astronomy was thorough. In 5 sections, his monumental work progresses through native Indian astronomy and culminates in 2 treatises on Western astronomy, showing calculations based on Greek and Alexandrian reckoning and even giving complete Ptolemaic mathematical charts and tables. Encyclopædia Britannica (2007) s.v.Varahamihira
 ^ History of astronomy in India. Indian National Science Academy. pp. 85, 114, 345.
 ^ Velandai Gopala Aiyer. The chronology of ancient India: beginning of the Sat Yuga, Dwaper, Treta, and Kali Yuga with date of Mahabharata. Sanjay Prakashan. p. 63.
 ^ MonierWilliams. "Definition of म्लेच्छ, MonierWilliams".
 ^ "History of Mathematics in India".
 ^ "Varahamihira".
 ^ "History of Mathematics in India".
 ^ J J O'Connor & E F Robertson. "Varahamihira".
 ^ "Varahamihira".
External links
 O'Connor, John J.; Robertson, Edmund F., "Varāhamihira", MacTutor History of Mathematics archive, University of St Andrews.
 Pancasiddhantika, Brihat Jataka, Brihat Samhita and Hora Shastra Various editions in English and Sanskrit. (PDF)
 The Brihat Jataka (1905) Pdf edition internet archive

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