I was thinking what I should post as the first post in the Mathematics category. To tell you the truth I had something else in mind, but I will most probably post that as the next post in this category. So, coming back to the point I think I will start with numbers the building block of Mathematics. I will tell you about some of my favorite numbers.
The Hardy-Ramanujan Number: 1729 is the Hardy-Ramanujan number. There is a very interesting anecdote associated with this, let’s talk about that. Hardy writes about one his visits to Ramanujan, he states, “I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.”
The two ways are:
1729= 123 + 13
&
1729=103 +93
But this is when negative cubes are not taken into account, as taking cube of negative number the smallest number that is sum of two cubes in two different ways is actually 91. I am not writing how, so it’s kind of homework for you folks. I also have obvious fascination about pi and tau. Let’s talk about them later. Do you get what I am saying? (Spoiler Alert: My second story in this regard will be related to these two majestic numbers.)
Avogadro Number: 6.022x 10^23 is the Avogadro number. Named after the Italian scientist Amedeo Avogadro, this number has utmost importance in science. This number gives the number of constituent particles in 1 mole of the substance.
There are many in this list, but I am not going to bore you out with my personal fascination with some numbers, that you might not find that much fascinating. Let’s talk about some other good stuff.
When I was in grade 5, I had this idea that I had found this amazing relation between square of numbers. But to my bewilderment, and thanks to Mr. Internet I found out that this is actually a very fundamental thing related to powers, and most people are aware of it.
So, let’s write down a list of squares:
02= 0
12=1
22=4
32=9
42=16
Now let me write the relation that I “supposedly” discovered as a child in 5th grade:
12-02=1
22-12=3
32-22=5
42-32=7
Do you see a relation in that? The difference between consecutive square is a consecutive odd number. Do you feel it’s magic? Then my friend you cannot be further than the truth. So for your understanding, look at the following diagram, and you will get what is really happening.
