Aryabhatiya

Aryabhatiya (IAST: Āryabhaṭīya) or Aryabhatiyam (Āryabhaṭīyaṃ), a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata.

Philosopher of astronomy Roger Billard estimates that the book was composed around 510 CE based on historical references it mentions.

[1][2] Aryabhatiya is written in Sanskrit and divided into four sections; it covers a total of 121 verses describing different moralitus via a mnemonic writing style typical for such works in India (see definitions below): It is highly likely that the study of the Aryabhatiya was meant to be accompanied by the teachings of a well-versed tutor.

That is, he used letters of the Devanagari alphabet to form number-words, with consonants giving digits and vowels denoting place value.

In the final section, the "Gola" or "The Sphere," Aryabhata goes into great detail describing the celestial relationship between the Earth and the cosmos.

The treatise uses a geocentric model of the Solar System, in which the Sun and Moon are each carried by epicycles which in turn revolve around the Earth.

Aryabhata's methods of astronomical calculations have been in continuous use for practical purposes of fixing the Panchangam (Hindu calendar).

For example Ganitanand in [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V = Ah/2V=Ah/2 for the volume of a pyramid with height h and triangular base of area AA.

This relates to verses 6, 7, and 10 of the second section of the Aryabhatiya Ⓣ and in [13] Elfering produces a translation which yields the correct answer for both the volume of a pyramid and for a sphere.