Monday, November 10, 2008
Quadratic Equation, Algebra And Permutation Combination
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.
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!
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.