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Math: Problem of the day-2

December 18, 2009 - 5:10 PM

Posted in Algebra, Mathematics | 3 comments

This problem was asked in IMO 1970, Hungary.
Q: For what natural numberscan the product of some of the numbersbe equal to the product of the remaining ones?
Note that since there are 6 numbers under consideration, if a prime numberdivides any of these numbers, it cannot be greater than 5.
In the set of numbers there can [...]

Math: Problem of the day-1

December 17, 2009 - 6:04 PM

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Posted in Geometry, Mathematics | 4 comments

This problem was asked in IMO 1961, Hungary.
Q: Letbe the lengths of a trianglewhose area is Prove that In what case does equality hold?
Solution: We can express the area in terms of the sides and angles of the triangle:

Also, the cosine rule says that

Therefore,

Note that equality will hold above ifand that is, when the triangle [...]

On infinity

November 12, 2009 - 4:31 PM

Posted in Reflections | 2 comments

Infinity, represented as ∞ is a concept in mathematics and philosophy that refers to a quantity without any bound. Infinity is a strange concept, and has many intriguing implications.

A subset of an infinite set can be put into one-to-one correspondence with the original set. For example, the set of natural numbers and the set of even [...]

Is God a chemist

October 6, 2009 - 8:36 PM

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Posted in Chemistry | 4 comments

Experimental science is difficult to comprehend and Chemistry is one of the oldest experiment based science. There are innumerable examples of chemical reactions in our daily life. The chemical reaction between the LPG and the air in the kitchen keeps the flame burning. The flame gives heat energy for cooking and even the food we [...]

Physics: Problem of the day-19

June 18, 2009 - 3:30 PM

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Posted in Heat and Thermodynamics, Physics, Problems in Physics | 1 comment

Q. A gas takes part in two thermal processes in which it is heated from the same initial state to the same final temperature. The two processes are represented on a p – V diagram by straight lines 1 →2 and 1 → 3:
In which process is the amount of heat supplied to the gas [...]

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