Favorite Irrational Number

[Jet Black]

For example, I claim it is impossible to construct a line of length $pi$.

of course it is possible. first construct a line of arbitrary length, then redefine your units so the line is of length pi.

 

[Arikay]

Sure it can. (I think. )

Make a perfect circle, make a cut in it, stretch it out into a line. There ya go. Measuring it accuratly though is another question all together.

Edit: forgot to add that the Diameter of the circle needs to be 1 unit.

For me "exists" means "can be constructed in a finite number of steps". I do not doubt the theory of irrational numbers. I do, however, deny that they can be constructed. For example, I claim it is impossible to construct a line of length $pi$.

 

[Jet Black]

oh, and if you want to argue you can't have a perfect circle, then take a black hole of diameter 1, and it will have a circumfrence of exactly pi.

 

[Orihalcon]

i forgot my math definitions a while ago... lol

heyhey, a singularity with a diameter!

 

[sad astronaut]

Did you know that e^ipi = -1?

That is true. You must be into math. Are you a college student?

 

[Philip]

of course it is possible. first construct a line of arbitrary length, then redefine your units so the line is of length pi.

Nope. That doesn't work. In doing so, you have a undefined unit.

 

[Philip]

oh, and if you want to argue you can't have a perfect circle,

Yes, that is a necessary conclusion.

then take a black hole of diameter 1, and it will have a circumfrence of exactly pi.

Nope. All the mathematics surrounding what we know of black holes presupposes the existence of irrational numbers, not to mention all other forms of limits.

This is not to say that irrational numbers do not serve a purpose in modeling reality. I do, however, claim that any use of irrational numbers contains an inherent approximation.

 

[Duane Morse]

Phi.

Square root five plus one, divided by two.

1.6180339887498948482045868343656

to so many places.

You can also calculate it using the Fibonacci Series of numbers. The ratio between sucessive pairs comes ever closer to Phi.

It begins 0, 1, 1, 2, 3, 5, 8, 13...

Each is the sum of the previous two.
So the ratios go like this:

0
1 #DIV/0!
1 1
2 2
3 1.5
5 1.666666667
8 1.6
13 1.625
21 1.615384615
34 1.619047619
55 1.617647059
89 1.618181818
144 1.617977528
233 1.618055556
377 1.618025751

 

[Frumious Bandersnatch]

I voted for e because the exponential function is immune to differentiation and so important in kinetics. Plus I once published the solution of an exponential rate equation and won a minor award for the paper that inclued a few bucks. Always follow the money.

The Frumious Bandersnatch

 

[PhantomLlama]

That is true. You must be into math. Are you a college student?

No, but I hope to be (aiming for physics of some kind). My sister (going to do maths at Cambridge this year) told me the e^ipi = -1 factlet.

About the black hole, the distortion effect of its gravity means the diameter is more than 1. To use the traditional rubber sheet analogy, if you draw a circle on a rubber sheet then put a ball in the middle, it stretches the sheet, so measuring it gives a distance of more than 1.

I think.

 

[sad astronaut]

As far as if irrational numbers exist in reality... I may be pretending to know more than I actually do, but... Since matter is broken up into discrete units, and is not continuous, wouldn't it actually be impossible to have something with a length of pi? Pi has an infinite number of decimal places, whereas units of space or time can only be broken down so small.

 

[Jet Black]

As far as if irrational numbers exist in reality... I may be pretending to know more than I actually do, but... Since matter is broken up into discrete units, and is not continuous, wouldn't it actually be impossible to have something with a length of pi? Pi has an infinite number of decimal places, whereas units of space or time can only be broken down so small.

well it depends on where you start your definition (remember a measured length is arbitrary, things are only relative). There might not be any truly irrational numbers in nature, but I am not sure... Things like that probably get lost in the quantum fuzziness anyway.

 

[obediah001]

There may not be irrational #'s but there are sure alot of irrational people about us!

 

[Jet Black]

Silence Troll!

 

[revolutio]

3.141592653589793238462643383279502

That is the best I can do from memory. The only thing I learned in Geometry.

 

[Mainframes]

I am going to have to vote for e because it is so useful. I use it constantly in engineering problems. Ah the joy of exponential decay of concentration within a reactor...

Plus it's easy to differentiate and integrate...!