The mathematics and astronomy of Āryabhaṭa, verse by verse
Āryabhaṭa encoded astronomical figures — millions of planetary revolutions — into single pronounceable Sanskrit syllables, so a whole almanac could be carried as memorised verse.
Type any Devanagari word or number and watch it convert, syllable by syllable.
Composed by Āryabhaṭa in 499 CE, when he was twenty-three, the आर्यभटीय compresses a complete system of mathematics and astronomy into 121 verses across four pādas. It opens the decimal place-value era, gives an accurate value of π, tabulates the sine, models the planets with epicycles, and argues — a thousand years before Copernicus — that the Earth turns on its axis. Read each chapter below; tap any Sanskrit word to reveal its meaning or resolve Āryabhaṭa's alphabetic numerals.
गणित · काल · गोल — mathematics, the reckoning of time, and the sphere
The foundational constants: planetary revolutions per yuga, orbital sizes, the obliquity of the ecliptic, epicycle tables, and the unique alphabetic numeral system.
Read the verses → 33 versesPure mathematics: place value, square and cube roots, areas and volumes, the value of π, the sine table, series, and the kuṭṭaka pulverizer for indeterminate equations.
Read the verses → 25 versesThe reckoning of time: units from year to prāṇa, yugas and intercalation, the order of the planets, and the eccentric–epicycle model that yields true positions.
Read the verses → 50 versesSpherical astronomy: the celestial sphere, the Earth's rotation, the armillary sphere, declination and gnomon problems, parallax, and the computation of eclipses.
Read the verses →how the ideas connect across the chapters
the verses staged as running simulations you can open live
Sixteen animated scripts that rebuild Āryabhaṭa's geometry in Gol · Astro Lab — obliquity, epicycles and planet cycles from the Gītikā; the Earth's rotation, reference circles, declination, precession and eclipses from the Gola; the rising of the signs and retrograde motion from the Kālakriyā. Run each one in the browser, or read its source.
Open the Gol tour → 9 scriptsNine scripts that stage the model itself in Mandal · मण्डल — the geocentric ↔ heliocentric duality of the śīghra epicycle, the Moon's nodes and apsis, synodic versus sidereal months, eclipses at the node, the Saros cycle, precession and the solar year. Run each one in the browser, or read its source.
Open the Mandal tour →take the number system with you