Department of Mathematics, University of Sri Jayewardenepura
In Mathematics world, irrational numbers play a controversial role. If a number cannot be written as a division of two integers, then it is called an irrational number. √2 is the most common example in this regard.
Now, what is the incredible aspect of these irrationals? It comes with decimal representation of irrationals. The decimal representation of an irrational number belongs to infinite decimal category. This reveals that numerically, an irrational number cannot be interpreted exactly. For an instance, √2 has its decimal representation as 1.4142135……, where there is no termination or pattern to understand the numerical value. So, can we tell exactly what the amount √2 comprises? No, we cannot. But, surprisingly we can draw a length of √2 units exactly. Just think of the diagonal of a rectangular bilateral triangle with sides other than to diagonal are of unit length. According to the Pythagoras Theorem, it is √2. What a strange moment! We cannot tell what √2 is, but we can draw it in a paper! Is it a magic cheating our eyes?
Try this magic with more and more irrationals. If you hunt more, you get more.
No comments:
Post a Comment