Mathematician:Bhaskara II Acharya

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Indian mathematician and astronomer.

One of the first to identify zero as a number in its own right.

He was so influential that his works were still being copied by as late as $1800$.




  • Born: 1114 in Vijayapura, near Bijjada Bida (in present day Bijapur district, Karnataka state), South India
  • Died: 1185 in Ujjain, India

Theorems and Definitions

  • A proof of Pythagoras' Theorem by dropping a perpendicular and investigating the relations between the ratios of the sides of the resulting similar triangles.

Results named for Bhaskara II Acharya can be found here.


All written in ca. $1150$:

  • Lilavati ("The Beautiful", about arithmetic, in particular rules for divisibility by $9$, $3$, $5$, $7$ and $11$)
  • Siddhanta Shiromani (or Siddhantasiromani) which consists of two parts:
    • Goladhyaya (sphere)
    • Grahaganita (mathematics of the planets).
It contains sine tables and various trigonometric relations.
  • Vasanabhasya of Mitaksara (Bhaskara's own commentary on the Siddhanta Shiromani)
  • Karanakutuhala (Calculation of Astronomical Wonders) or Brahmatulya (a simplified version of the Siddhanta Shiromani)
  • Vivarana (a commentary on the Shishyadhividdhidatantra of Lalla.

Notable Quotes

-- on demonstrating a proof of Pythagoras's Theorem

The second value is in this case not to be taken, for it is inadequate; people do not approve of negative roots.
-- on negative roots

Also known as

In Kannada: ಭಾಸ್ಕರಾಚಾರ್ಯ

The name can also be rendered Bhāskara.

Known as Bhāskara II, Bhāskara Āchārya ("Bhāskara the teacher"), or Bhāskarāchārya, to distinguish him from Bhaskara I).