Veṇvāroha is a work in

Sanskrit Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late ...

composed by Mādhava of Sangamagrāma ( – ), the founder of the

Kerala school of astronomy and mathematics The Kerala school of astronomy and mathematics or the Kerala school was a school of Indian mathematics, mathematics and Indian astronomy, astronomy founded by Madhava of Sangamagrama in Kingdom of Tanur, Tirur, Malappuram district, Malappuram, K ...

. It is a work in 74 verses describing methods for the computation of the true positions of the

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

at intervals of about half an hour for various days in an anomalistic cycle. This work is an elaboration of an earlier and shorter work of Mādhava himself titled '' Sphutacandrāpti''. ''Veṇvāroha'' is the most popular astronomical work of Mādhava.

Etymology

The title ''Veṇvāroha'' literally means '

Bamboo Bamboos are a diverse group of evergreen perennial flowering plants making up the subfamily Bambusoideae of the grass family Poaceae. Giant bamboos are the largest members of the grass family. The origin of the word "bamboo" is uncertain, bu ...

Climbing' (''Veṇu'' 'bamboo' + ''āroha'' 'climbing') and it is indicative of the computational procedure expounded in the text. The computational scheme is like climbing a bamboo tree, going up and up step by step at measured equal heights.

Overview

It is dated 1403 CE. Acyuta Piṣārati (1550–1621), another prominent

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...

of the Kerala school, has composed a

Malayalam Malayalam (; , ) is a Dravidian language spoken in the Indian state of Kerala and the union territories of Lakshadweep and Puducherry (Mahé district) by the Malayali people. It is one of 22 scheduled languages of India. Malayalam was des ...

commentary Commentary or commentaries may refer to: Publications * ''Commentary'' (magazine), a U.S. public affairs journal, founded in 1945 and formerly published by the American Jewish Committee * Caesar's Commentaries (disambiguation), a number of works ...

on ''Veṇvāroha''. This astronomical treatise is of a type generally described as Karaṇa texts in

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

. Such works are characterized by the fact that they are compilations of computational methods of

practical astronomy Pragmatism is a philosophical tradition that considers words and thought as tools and instruments for prediction, problem solving, and action, and rejects the idea that the function of thought is to describe, represent, or mirror reality. P ...

. The novelty and ingenuity of the method attracted the attention of several of the followers of Mādhava and they composed similar texts thereby creating a genre of works in Indian mathematical tradition collectively referred to as ‘veṇvāroha texts’. These include ''Drik-veṇvārohakriya'' of unknown authorship of epoch 1695 and ''Veṇvārohastaka'' of Putuman Somāyaji. In the technical terminology of astronomy, the ingenuity introduced by Mādhava in ''Veṇvāroha'' can be explained thus: Mādhava has endeavored to compute the true

longitude Longitude (, ) is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter l ...

of the Moon by making use of the true motions rather than the epicyclic astronomy of the

Aryabhata Aryabhata (ISO: ) or Aryabhata I (476–550 CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta Era and produced works such as the ''Aryabhatiya'' (which ...

tradition. He made use of the anomalistic revolutions for computing the true positions of the

using the successive true daily velocity specified in '' Candravākyas'' (Table of Moon-mnemonics) for easy memorization and use. Veṇvāroha has been studied from a modern perspective and the process is explained using the properties of periodic functions.

Etymology

Overview

See also

References

Further reading