SHORT TRICKS USING SYMMETRY Symmetry is the most beautiful gift that we have from nature. Symmetry is what we see at a glance. Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand the nature. Gradually, they have become the backbone of our theoretical formulation of physical laws. Nature seems to take advantage of the simple mathematical representation of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of symmetry laws never fails to develop. As we discover more and more about our environment and our surroundings, we see that nature can be described mathematically. The beauty of flowers, the majesty of a tree, even the rocks upon which we walk can exhibit nature’s sense of symmetry. Mathematically, speaking extremity is obtained when the things under consideration are symmetrical. For example, the product of two numbers, when sum is given, will be the largest when the numbers are symmetrical i.e. equal. Among all rectangles of a given parameter the most symmetrical figure (square) has the largest area. The triangle of maximum area that can be inscribed in a given circle is again the most symmetrical triangle i.e. equilateral triangle. There are always questions asked in competitive exams which use the symmetry to solve them. Q- The mth term of an AP is n and its nth term is m. then its pth term is (A) m – n –p (B) m – n + p (C) n – m + p (D) m + n – p Sol- Since the question is symmetrical in terms of m and n both. So the answer has to be symmetrical in terms of m and n.
Posted on: Sun, 15 Sep 2013 09:43:50 +0000
Trending Topics
Recently Viewed Topics
© 2015