Showing posts with label Mathematical curiosity. Show all posts
Showing posts with label Mathematical curiosity. Show all posts

Friday, 14 March 2014

Achilles and the Tortoise

I have many varied interests, some of them you know, Some of them I know, some I dare not admit to myself and some may well forever remain unidentified. But of all of them one is a curious liking to obscure paradoxes. I like the inconclusivity of them, the sheer reluctance of them to conclude to something, the ambiguity they persists and the infinite admiration that it invokes. Be it the time travelers paradox that effectively renders him a silent spectator of ages past or the Achilles paradox pointed out by the greek philosopher Zeno that is so obviously untrue yet mathematics require obscure concepts to prove it so. I take pride in the fact that these concepts are elusive and obscure to many it makes sense to me.

Now the paradox of Achilles I'd something that captured my imagination for sometime now, I will let my readers enjoy and revel in it's magnificence while I go and pen down something worth while.

In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.

PS : I was so lazy that I effectively copied the while definition of this paradox outright from Wikipedia.

Saturday, 15 September 2012

My Love with Fractals

Fractal wallpaper 1

Ever since I knew myself I was in love with science and its very diverse aspects. The various mysteries that it upheld and the many fascinating ideas that emerged from it. I always found it both interesting and engaging to chase around science and technology. This urge to know has always been as much part of me  as anything else, even my passion for writing. Its one side of me that I often do not ponder in my writings ever. The reason to bring it up now is of immense beauty, both in its meaning and its aesthetics. The reason is fractals.

For anyone who does not know what a fractal is the layman explanation is of utmost simplicity. A fractal is anything that is self repeating , That is if we have such an image that when zoomed in represents closely the original image then it is called a fractal. My introduction to fractals happened some years back when I was casually watching a soap opera. I just heard a character mention fractals as his mathematical curiosity and that caught my attention and then I was head over heels into fractals.

Nevertheless my inquiry into the world of fractals showed me many things including that of some very cleverly hidden secrets of the natural world. If you must know, fractals are everywhere around us, Fractal patterns determine how the blood vessels branch and how the snow is formed, one would never imagine its significance in the world. Any how that is not what I am here to tell you, this has to be told to   you by a mathematical wizard and I am not one. I am just here to point out to you the wonderful and beautiful world of fractals and I believe nothing could attain that edge than these pictures I happened to collect from the internet. 

Fractal wallpaper 2

Fractal wallpaper 3

Fractal wallpaper 4

Fractal wallpaper 5

Fractal wallpaper 6

Fractal wallpaper 7

Fractal wallpaper 8

Fractal wallpaper 9