Varahamihira is the Brihat-Samhita

Brihat – Samhita

Another important contribution of Varahamihira is the 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 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 daughter-in-law of Varahamihir.

Influences

The Romaka Siddhanta (“Doctrine of the Romans”) and the varahawere 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 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…..” (“mleccha hi yavanah tesu samyak shastram kdamsthitam/ rsivat te ‘p i pujyante kim punar daivavid dvijah” (Brihat-Samhita 2.15)).

Place values system and Zero interduce to world by Aryabhata

Mathematics

Place value system and zero

The palce values system, first seen in the 3rd-century Bakhshali was clearly in place in his work. While he did not use a symbol for Zero, the French mathematician Georges Ifrah   argues that knowledge of zero was implicit in Aryabhata’s  Palce – Values System as a place holder for the powers of ten with Null -Coefficient

However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic  tradition from  Vedic Times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sine’s in a mnemonic form.

Place values Chart

 

 Pi ( π ) values

Aryabhata worked on the approximation for pi, and may have come to the conclusion that is irrational. In the second part of the Aryabhatiyam (Ganitapada 10), he writes:

Caturadhikam satama stagunam devasa stistatha sahasranam

Ayutadayavi siambhasyasanno vittaparinahah


“Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached.”

This implies that the ratio of the circumference to the diameter is ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figure.

OR

Aryabhatta

chaturadhikaM shatamaShTaguNaM dvAShaShTistathA sahasrANAm AyutadvayaviShkambhasyAsanno vr^ttapariNahaH.
[gaNita pAda, 10] Aryabhatiyam (499 CE)
“Add 4 to 100, multiply by 8 and add to 62,000. This is approximately the circumference of a circle whose diameter is 20,000.”
i.e.
correct to four places.

 

It is speculated that Aryabhata used the word ‘asana’ (approaching), to mean that not only is this an approximation but that the value is incommensurable (or irrational). If this is correct, it is quite a sophisticated insight, because the irrationality of pi was proved in Europe only in 1761 by “Lambert”.

After Aryabhatiya was translated into Arabic  (c. 820 CE) this approximation was mentioned in Al-Khwarizmi’s  book on algebra.

he value of pi is being used in India from ancient times. It gives us an insight about how evolved our past was. There is a shloka, a hymn to Lord Krishna or Shiva, which gives the value of pi upto 31 decimal places.

Its amazing that our forefathers used an encryption technique to easily remember it. What is more astonishing is that they needed pi upto 31 places.

Importance of Pi
Pi deals with circles and circles are very important in many fields. Pi is a very important number in the fields of :

  • Geometry and trigonometry,
  • Complex number and analysis,
  • Number theory,
  • Nrobability and statistic physics,
  • Engineering and geology.
  • Computers and many more
  • Katapayadi Encryption
  • gopiibhaagya madhuvraataH shruMgashodadhi saMdhigaH .
    khalajiivitakhaataava galahaalaa rasaMdharaH
  • This shloka, a hymn to Lord Krishna or Shiva, gives the value of pi upto 31 decimal places.
Pi using Encryption
  • • Katapayadi system is used to encode numbers in many shlokas

    ga – 3 pii – 1 bhaa – 4 gya – 1 ma – 5 dhu – 9 ra – 2 ta -6 shru – 5 ga – 3 sho – 5 da – 8 dhi – 9 sa – 7 dha – 9 ga – 3 kha – 2 la – 3 jii – 8 vi – 4 ta – 6 kha – 2 ta – 6 va – 4 ga – 3 la – 3 ra – 2 sa – 7 dha – 9 ra – 2

    pi = 3.1415926535897932384626433832792

 

to be continue …….2

Indian Mathematician and astronomer Brahmagupta

BrahmaguptaBrahmagupta (598–.670 CE) was an Indian Mathematician and astronomer who wrote two important works on Mathematics and Astronomy: the Brahmaphutasiddhanta (Extensive Treatise of Brahma) (628), a theoretical treatise, and the Khandakhadyaka, a more practical text. There are reasons to believe that Brahmagupta originated from Bhinmal. the Durkeamynarda in 672. The Brahmasphutasiddhanta (Corrected Treatise of Brahma) is arguably his most famous work. The historian al-Biruni (c. 1050) in his book Tariq al-Hind states that the Abbasid caliph al-Ma’mun had an embassy in India and from India a book was brought to Baghdad which was translated into Arabic as Sindhind. It is generally presumed that Sindhind is none other than Brahmagupta’s Brahmasphuta-siddhanta.

Brahmagupta was the first to give rules to compute with Zero. The texts composed by Brahmagupta were 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

the application of mathematics to the physical world, rather than about the mathematics itself. In Brahmagupta’s case, the disagreements stemmed largely from the choice of astronomical parameters and theories. Critiques of rival theories appear throughout the first ten astronomical derived.

Although Brahmagupta was familiar with the works of astronomers following the tradition of Aryabhatta, it is not known if he was familiar with the work of Bhaskara I, a contemporary. Brahmagupta had a plethora of criticism directed towards the work of rival astronomers, and in his Brahmasphutasiddhanta is found one of the earliest attested schisms among Indian mathematicians. The division was primarily about chapters and the eleventh chapter is entirely devoted to criticism of these theories, although no criticisms appear in the twelfth and eighteenth chapters.

to be continues…..

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

varaha

Varahamihira’s Contributions of Trigonometry

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

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.

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.

Optics

Among Varahamihira’s contribution to physics is his statement that reflection is caused by the back-scattering 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.

^ “the Panca-siddhantika (“Five Treatises”), a compendium of Greek, Egyptian, Roman and Indian astronomy. Varahamihira’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.

to be continue……

Varahamihira is the Brihat-Samhita

 

 

varahaBrihat – Samhita

Another important contribution of Varahamihira is the 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 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 daughter-in-law of Varahamihir.

Influences

The Romaka Siddhanta (“Doctrine of the Romans”) and the Paulisa Siddjanta (“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 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…..” (“mleccha hi yavanah tesu samyak shastram kdamsthitam/ rsivat te ‘p i pujyante kim punar daivavid dvijah” (Brihat-Samhita 2.15)).

 

to be continues………….

Varahamihira, was an Indian astronomer, Indian astronomer, mathenatician, and astrologer

Varahamihira an Indian astronomer

Varahamihira वराहमिहिर) (505–587 CE- India), also called Varaha or Mihir, was an Indian astronomer, mathenatician, and astrologer and who lived in Ujjain. He was born in Avanti 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 (Navarata (Navaratnas)) of the court of legendary ruler Yoshdharman Vikramaditya of Malwa.

Works

He was the first one to mention in his work Pancasiddhantika that the avanamsa, or the shifting of the equinox, is 50.32 seconds.

Pancha-Siddhantika

Varahamihira’s main work is the book Pancasiddhantika (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, Vasihtha Siddhanta and Paitamaha Siddhantas . It is a compendium of Vedanga Jyotisha as well as Hellenistic astronomy (including Greek, Egyptian and Roman elements). 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 Alberumi also described the details of “The Five Astronomical Canons”:

“They [the Indians] have 5 Siddhantas :

  • Surya Siddhanta, ie. The Siddhanta of the Sun, thought to be composed by Latadeva, ,but actually composed by Mayasura also known as Mamuni Mayan as stated in the text itself.
  • Vasishtha-Siddhantas , so called from one of the stars of the Great Bear, composed by Vishnucandra,
  • Paulisa- Siddhanta , so called from Pulisa, the Greek, from the city of Saintra, which is supposed to be Alexandria, composed by Pulisa.
  • Romaka- Siddhanta , so called from the Rūm, ie. the subjects of the Roman Empire, composed by srishen .
  • Paitahama- Siddhanta.

 

to be continue…..

 

Bhaskara II Astronomy Therory

Bhaskara II Astronomy

Using an astronomical model developed by Brahmagupta in the 7th century, Bhaskara accurately defined many astronomical quantities, including, for example, the length of the sidereal year, the time that is required for the Earth to orbit the Sun, as 365.2588 days which is the same as in Suryasiddhanta. The modern accepted measurement is 365.2563 days, a difference of just 3.5 minutes.

His mathematical astronomy text Siddhanta Shiromani is written in two parts: the first part on mathematical astronomy and the second part on the sphere.

The twelve chapters of the first part cover topics such as:

  • Mean longitudes of the planets.
  • True longitudes of the planets.
  • The three problems of diurnal rotation.
  • Suzgies .
  • Lunar eclipses.
  • Solar Eclipses.
  • Latitudes of the planets.
  • Sunrise equation
  • The Moon’s crescent.
  • Conjunctions of the planets with each other. The second part contains thirteen chapters on the sphere. It c
  • Conjunctions of the planets with the fixed stars.
  • The paths of the Sun and Moon.
  • overs topics such as:
  • Praise of study of the sphere.
  • Nature of the sphere.
  • Cosmography and geography.
  • Planetary and geography.
  • Planetary mean motion.
  • Eccentric epicyclical mode of the planets.
  • The armillary sphere.
  • Spherical Trigonometry .
  • Ellipse calculations.
  • First visibilities of the planets.
  • Calculating the lunar crescent.
  • Astronomical instruments.
  • The Seasons.
  • Problems of astronomical calculations.bhaskaracharya

 

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