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Applied Mathematics

published on February 26th, 2007 . by Vanaja

Applied mathematics is the application of pure mathematics in the service of a given purpose. It has some direct or practical application to objects and happenings in the material world. It plays a great role in the development of various subjects. Every discovery in science owes much to applied mathematics. Principles of applied mathematics have been useful in the investigation of such phenomenon as heat , sound, light, optics,navigation and astronomy. applied mathematics is a part of mathematics definitely related to or suggested by some tangible situations, though not always intended for practical use. It is the connecting link between pure mathematics on one side, physical, biological, social sciences and technology on the other.

Pure Mathematics

published on February 20th, 2007 . by Vanaja

Pure mathematics involves systematic and deductive reasoning. It treats only theories and principles without regard to their application to concrete things. It is developed on an abstract, self contained basis without any regard to any possible kind of practical applications that may follow. It consists of all those assertions as that if such and such proposition is true of anything,such and such another proportion is true of that thing.

The Chess Board

published on February 3rd, 2007 . by Vanaja

We all know that a chess board has 64 squares. This can be completely covered by 32 cardboard rectangles, each cardboard covering just 2 squares.

Supposing we remove 2 squares of the chess board at diagonally opposite corners, can we cover the modified board with 31 rectangles? If it can be done, how can we do it? And if it cannot be done, prove it impossible.
Answer
No.It can not be done.
Each rectangle covers one white square and one black square, because on a chess board the white and black squares are always adjacent.
I think now you gor the reason.