Ancient Indian Mathematicians and Their Teachings

We are starting a very special series “Teaching of Indian Mathematicians”.

In this special series we will discuss various concepts propounded by Indian mathematicians which are very useful even today.

**Formula for cyclic quadrilateral propounded by 9 ^{th} Century Indian Mathematician Mahavira**

First in this series, I am explaining a very nice concept propounded by **Mahavira**, a 9th-century Indian mathematician from Gulbarga (South India) who asserted that the square root of a negative number did not exist. He gave the sum of a series whose terms are squares of an arithmetical progression and empirical rules for area and perimeter of an ellipse. Mahavira’s eminence spread in all South India and his books proved inspirational to other Mathematicians in Southern India.

One of his teachings gives us Formula for cyclic quadrilateral. He established equations for the sides and diagonal of Cyclic Quadrilateral.

**Definition of Cyclic Quadrilateral: **a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. In a cyclic quadrilateral, opposite angles are supplementary (their sum is ? radians or 180°). Alternatively, each exterior angle is equal to the opposite interior angle

If sides of Cyclic Quadrilateral are *a*,*b*,*c*,*d* and its diagonals are *x* and *y* while

Then, xy = ac + bd

All of the readers of Quickermaths.com are requested to participate in the above series by sending us similar concepts they come across in their studies and/or research on mathematics field. Please also let us know your name, qualifications and city. We will post those in Quickermaths.com with due appreciation for the contributor.

Hope this will enrich our knowledge of mathematics and give a boost to the feeling of pride for our ancient Indian Mathematicians.

Thanks in advance for your kind and generous input.

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