Around-n-around we go, When we meet we have a zero !

What do you think is the most powerful tool we possess as human being?...any thoughts?

Yes it is definitely this power of thinking, the power of imagination that we possess - the greatest gift that we are privileged to have. We live in this mere 3 dimensional world and see how beautifully we have extrapolated our ideas to portray the multi-dimensional universe. But behind these theories, hypothesis or 'imaginations', the backbone has always been mathematics and its elegant equations and the fundamental of which are numbers. Numbers never lie and so does the mathematics. So let's take a voyage in this ocean of truth today !

Numbers and therefore counting are integral part of our daily life. Even these words that you are now reading on the screen have been coded with a series of zero's and one's. But it is an interesting story as how these digits and numbers came to dominate our world.


Presently, the earliest known archaeological evidence of any form of writing or counting are scratch marks on a bone from some 150,000 years ago. But the first really solid evidence of counting,in the form of the number 'one', is from a mere twenty-thousand years ago. An ishango bone was found in the Congo with two identical markings of sixty scratches each and equally numbered groups on the back.These markings are a certain indication of counting. Thus to find out an answer to the question of 'how many?' created this idea of distinguishing objects accordingly a.k.a counting.


Now, let's take the example of the number 'pi'. As we all know that the number 'pi' is a mathematical constant, the ratio of a circle's circumference to its diameter commonly approximates as 3.14159. In other words 'pi' is the number of times a circle's diameter will fit around the circle's circumference. Seems simple. So what will be the number of times shall the diameter fit around the circumference? Finite number of times, correct? But hey 'pi' is a number with no ends ! Intriguing, right? Let's dig a bit deeper.


So we can see from the image that the number will go on and on. Infact, this property of 'pi' is used to test the stress capacity of modern day supercomputers. Thus 'pi' is said to be a transcendental number in simpler words not an algebraic number. But for this it doesn't lose its valour rather its importance rose to a different level. These transcendental numbers are very much useful in the study of straightedge-and-compass constructions, particularly in proving the impossibility of squaring the circle.

Taking a scale and a compass we can try to draw a square which equals the area of a circle. Unfortunately, it is impossible to construct a square with area equal to the area of any given circle, including 1π, using only a straightedge and a compass, thus proving that π is transcendental. It so unique !


This is the Great Pyramid at Giza. The fascinating idea about this pyramid is the pyramid seems to approximate 'pi'. This means that the vertical height of the pyramid has the same relationship with its base as that of a diameter of a circle has with its circumference !




Thus mathematics holds the secret of understanding the world around us.

Let's take the example of Fibonacci numbers now.

From the standpoint of calculations it is easy to understand the collection, viz:

1 1 2 3 5 8 13 21 34 55...

We all know these, now let us visualize the various beautiful combinations of fibonacci numbers. Let's start by squaring the first few fibonacci numbers.

1   1   2   3    5     8      13       21      34       55..

1   1   4   9   25   64    169    441    1156   3025..

It's of no surprise that when we add the fibonacci numbers we arrive at the next fibonacci numbers as expected. But what about adding up its square? Lets look into it...

1 + 1 = 2

1 + 4 = 5

4 + 9 = 13

9 + 25 = 34 and the pattern continues...

See we got the fibonacci sequence by skipping a number inbetween.

Now let's see another one.

1 + 1 + 4 = 6

1 + 1 + 4 + 9 = 15

1 + 1 + 4 + 9 + 25 = 40

1 + 1 + 4 +9 + 25 + 64 = 104

Now look at the numbers. Yes, they are not fibonacci numbers. But if we closely observe them, see they are composed of fibonacci numbers.

6 = 2 * 3

15 = 3 * 5

40 = 5* 8

104 = 8 * 13

2..3..5..8..13..fibonacci numbers, right?

But why shall be sqr (1) + sqr (1) + sqr (2) + sqr (3) + sqr (5) + sqr (8) = 104 = 8 * 13 ?? 

Let's find it out with some basic geometry.

...now you can calculate the area yourself !  Thus we can prove the beautiful collection of fibonacci numbers.

Now if we continue to generate rectangle of such orders we shall go on generating rectangles of different areas.

Now have a look at this..

13 / 8 = 1.625

21 / 13 = 1.615..

34 / 21 = 1.619..

55 / 34 = 1.6176..

89 / 55 = 1.61818..

Thus we approach the golden ratio 1.61818033.. which has been fascinating us for all these years. This is because the nature around us follows the golden ratio. 

Such beautiful are the patterns, aren't so? So it's just numbers which gave rise to these wonderful shapes and patterns. Would you like to try this on a photo of yours? Go on if you may wish...

If we ponder a bit we shall also see that life has also got a pattern, an unique pattern of its own. Thus meditating or introspecting is so important, because at the end of the day its all about knowing our true self thus getting to know the pattern of our life and thus it is the way we shall get to know the true potential that lies hidden in us. Its also a game of numbers mixed with laws of physics, chemistry, biology and what not. That shall be the discussion for another day may be.

So coming back to the elegance of numbers, we know that an equation has two sides viz LHS and RHS

where, LHS = RHS, correct?

Now think of this..

  e^(i * pi) = (-) 1

It simply says that these two things on both the sides of '=' is negative one !

So (-)1 is negative one and at the same time, e^(i * pi) is also negative but imaginary !

You can ponder over it for a bit...

Magnificent isn't it? Its just about a matter of perspective. It matters how we would like to see the world around us.

So mathematics isn't all about calculation, rather its more about application, including the most important application of all as learning how to think.

"..Thus Mathematics isn't just solving for an unknown variable X but it's also about figuring out the Y (why ?).."

So although this world of mathematics is huge and vast, but its own elegant magical equations make it unprecedentedly beautiful. So before signing off let me share another elegant mathematical equation with you. 

The equation which defines the surreal idea of quantum entanglement.


Comments

  1. thereader10:13 PM, May 01, 2025

    Interesting color coding. So who is the author narrating to?

    ReplyDelete
    Replies
    1. Arunabha10:02 AM, May 02, 2025

      Dear esteemed reader , thank you for your time and thoughtful feedback.
      The author is simply narrating to the vast continuum of time , in the hope that some resonant frequency in this space-time fabric will stumble upon it, and feel the echo of the unspoken words.

      Delete

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