Monday, November 10, 2008

Quadratic Equation, Algebra And Permutation Combination


Algebra

A detailed analysis of ancient works brings to light the fact that the Shulba Sutras also called as Vedanga, is the origin of Algebra. Many discussions are there in Indian Algebra about solutions to linear equations and simultaneous equations. Even now we can identify the progress of Algebra in the construction of the sacrificial altars during sacrifices.

During Brahmagupta’s time, (700 A.D.) Algebra was called by different names such as Avyaktaganita, Bijaganita, Kuttaganita etc. probably algebra was known by different names in different places.

Qudratic Equation

Aryabhata, Brahmagupta and others knew how to solve the equation ax2 + bx +c = 0. Now the method we are using to solve quadratic equations was known to Sridharacharya of the 10th century A.D. His verse on this is as follows.


Permutation and Combination

In India, from times immemorial, the mathematical methods of permutation and combination are in use. These two methods were mainly used in literary compositions, vaastu, music and preparation of medicines.

nCr = n!
-----
r!(n-r)!

This common sutra has been written in the form of a verse by Karnataka’s mathematician Varahamihira in 9th century A.D.


In Vedic times, sages used to perform many types of sacrifices. Then problems regarding constructing different altars used to arise. To solve these problems, geometry was used because it clarified many matters relating to earth.

6 comments:

Satish said...

Vedas had sub categories in them called Upavedas. Branches like engineering, medical sciences; mathematics, astronomy and astrology etc were covered in them

One of the books which i use as reference for Vedic mathematics is by Jagadguru Swami Sri Bharati krishna Thirthaji Maharaja. This explains the sutras in simple and understandable language. However there aren't many illustrations and problems in the chapters

Btw i was reading an article on Vedic mathematics which explained calculus by use of sutras on quadratic equations.... a very interesting read it was

The language of Sanskrit also follows mathematics.... the verses were always composed in different meters (which is called CHANDHAS) which had logical rules set according to the breath taken to utter the words.

We can go on and on and on.....such is the beauty of Sanskrit. It is scientific as well as artistic....

Sowmya said...

Thnks Satish for the gyan :-)
I want to study Vedic mthematics... I will seek your guidance someday... :)

Sanjiv said...

u can learn Vedic mathematics from Shri Ramesh Kolluru, from Vedic Mathematics department of Ved Vignan Maha Vidya Peeth, The Art Of Living International Center, Bangalore.

Sowmya said...

Yeah Sanjiv, I think I saw a board on Kanakpura road. There are so many new things I am eager to learn.

Bharath NS said...

Vedic mathematics is good in the sense ... that we need to be proud of what our culture had provided to the world.... but comparing to western/modern mathematics it failed to evolve...

Bharath NS said...

Nevertheless nice post