‘Point- It seems to be more than an axiom!’ A different perspective!

Ankit Priyadarshi
7 min readDec 9, 2020

Hi guys, let's come to the point! :)

In mathematics, a point is defined as a dimensionless entity. In Euclidian geometry its an axiom, if we include the perspective of set theory, its a subset of space. I always wanted to understand why it was like this. In fact, while thinking about a different topic I think I understood why it is so!

I am going to share my understanding here, and request dear readers, your feedback on the same.

I was thinking about motion of objects and how to describe them, and how such ideas were conceived! As motion is a change of place of objects, we must have a clear way of differentiating between places (i.e. we should be more specific than ‘here’ and ‘there’). Generally we use co-ordinates for this, i was trying to understand the conception of this idea, which ultimately lead me to an understanding of ‘points’ as described below:

The below figure shows the three walls of my room, my desk and few other things. In my effort to understand co-ordinates I decided to choose a fixed place w.r.t which I would define the other places.

Let the fixed place be the centre of the wall clock. Now before we proceed we need to understand that we have assumed the centre of the clock as the fixed place, but it is not clear, what the dimensions of the centre are.

I mean how big is the centre? Or exactly which small black circle (see below figure) should represent the centre and why?

(In fact, we have no logical reason to choose a circle as well. But for the sake of simplicity, let a circle denote the centre. We will verify this idea when we have a better understanding.)

We know that it can’t be big enough to have a recognisable area and on the other hand it can’t be microscopic. So there should be of an optimum size to represent the centre.