Just had a thought today regarding PI. I'm not very good at geometry:
If π is irrational, does that means no one may ever draw a perfect circle?
This is just my assumption... .
Asked
Active
Viewed 461 times
-2
-
2$\sqrt{2}$ is irrational, but you can draw the hypotenuse of a right triangle with legs of length $1,1$. – user236182 Nov 22 '15 at 20:59
-
2Can you even draw a perfect line segment? A line segment of exactly $1$ cm? – Eff Nov 22 '15 at 20:59
-
1Well, if it helps. – quapka Nov 22 '15 at 21:07
-
4I see no logical connection between the mathematical fact that $\pi$ is irrational and the physical fact that no one can draw a perfect circle. – Andreas Blass Nov 22 '15 at 21:22
1 Answers
2
In my opinion, no one can even draw a perfect say line or point. Perfection is something present only in math (an abstraction). In the physical/real world, there's no such thing as a perfect line or a perfect circle. And this has nothing to do with $\pi$.
peter.petrov
- 12,568
-
I would say that someone can draw a perfect line but can't know it. – MoebiusCorzer Nov 22 '15 at 21:00
-
@MoebiusCorzer Well, I don't think so :) but probably you have some grounds for stating that. In fact a line has no thickness so ... as you draw it, you already know it's not perfect i.e. it's not really a line, it's a rectangle in the best case, and even that rectangle is not perfect :) because in some of its parts this rectangle is surely thicker (assuming you can measure it with great enough precision) than in other parts. – peter.petrov Nov 22 '15 at 21:01
-
1I think it is a matter of definition because "drawing a line" has no mathematical meaning, as far as I know. So speaking of the perfect line mathematically is not meaningful. I assumed that perfect meant "perfect in terms of measures", because it seemed to be the OP's consideration. Aside from that, I completely agree with you that it is not possible to physically (with atoms) draw the representation of a line such that the object drawn fits the mathematical property. – MoebiusCorzer Nov 22 '15 at 21:07
-
@MoebiusCorzer "drawing a line has no mathematical meaning, as far as I know" >>> OK, I agree, yes. Actually the whole statement has no formal math meaning due to this informal phrase "drawing a line" or "drawing a circle". – peter.petrov Nov 22 '15 at 21:19