# Mathematician:Bhaskara II Acharya

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## Contents

## Mathematician

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 $1800$.

## Nationality

Indian

## History

- 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.

- A proof of Pythagoras' Theorem by calculating the same area in two different ways and then canceling out terms to get $a^2 + b^2 = c^2$.

- Solutions of quadratic, cubic and quartic indeterminate equations.

Results named for **Bhaskara II Acharya** can be found here.

## Publications

All written in ca. $1150$:

*Lilavati*("The Beautiful", about arithmetic, in particular rules for divisibility by $9$, $3$, $5$, $7$ and $11$)

*Bijaganita*("Seed Arithmetic", about algebra and the solution of equations)

*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

*Behold!*- -- 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.*

## 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).

## Sources

- John J. O'Connor and Edmund F. Robertson: "Bhaskara II Acharya": MacTutor History of Mathematics archive

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.1$: The Pythagorean Theorem - 1992: David Wells:
*Curious and Interesting Puzzles*... (previous) ... (next): Indian Puzzles - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**Bhaskara**(1114-c.1185) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Bhaskara**(1114-c.1185) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $3$: Notations and Numbers: Brahmagupta, Mahavira and Bhaskara - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Bhāskara**(1114-85)