Favorite Irrational Number

[sad astronaut]

.

 

[SirKenin]

 

[jon1101]

pi, definitely. It's the only one I've bothered to memorize to several digits.

-jon

 

[Arikay]

3.1415926535897 (well 98 not 97 if you round. but I always tried to keep going)

thats as much as I have memorized. Talk about being way too board in math class like 3 years ago.

 

[NeilUnreal]

I had to go with the square root of two; it's so conveniently visible in diagonals.

-Neil

 

[Jet Black]

3.1415926535897 (well 98 not 97 if you round. but I always tried to keep going)

thats as much as I have memorized. Talk about being way too board in math class like 3 years ago.

bleh, I remembered pi to over 200 decimal places while doing a boring summer job. people kept asking me what these pieces of paper with numbers on them were, so I told them, they must have thought I was insane.

 

[imagineer]

You... *sniff* ...missed out 'i'.

 

[sad astronaut]

My personal favorite is e. It was found a long time ago but the fact that it shows up in compound interest formulas today (for interest compounded like every second) is really fascinating.

 

[Jet Black]

i is imaginary, not irrational

 

[sad astronaut]

i is imaginary, not irrational

Yes. Now if I had a poll asking for the coolest number ever, then 'i' would be my choice.

 

[PhantomLlama]

Did you know that e^ipi = -1?

 

[bagfullofsnakes]

My personal favorite is e. It was found a long time ago but the fact that it shows up in compound interest formulas today (for interest compounded like every second) is really fascinating.

I voted for e as well.

It always make me think of Andrew Jackson...not sure why, but 1828 always makes me think of Andrew Jackson.

 

[Orihalcon]

i is imaginary, not irrational

well, since irrational means you can't put it into a fraction, i would count as irrational because it's rather hard to make an imaginary number a fraction.

 

[jon1101]

well, since irrational means you can't put it into a fraction, i would count as irrational because it's rather hard to make an imaginary number a fraction.

But aren't irrational numbers by definition a subset of real numbers?

-jon

 

[imagineer]

I cannot be expressed in the form a/b, therefore it is irrational

 

[jon1101]

I cannot be expressed in the form a/b, therefore it is irrational

From Wikipedia, emphasis mine

In mathematics, an irrational number is any real number that is not a rational number, i.e., that cannot be written as a fraction a / b with a and b integers and b not zero.

http://www.wikipedia.org/wiki/Irrational_number

So, irrational numbers are by definition a subset of real numbers. Hence, i is excluded.

-jon

 

[Philip]

But aren't irrational numbers by definition a subset of real numbers?

Yes. The set of irrational numbers are, by definition, real. They are the numbers needed to complete the set of rational numbers.

BTW, as a constructivist, I deny the existence of irrational numbers.

 

[jon1101]

Yes. The set of irrational numbers are, by definition, real. They are the numbers needed to complete the set of rational numbers.

BTW, as a constructivist, I deny the existence of irrational numbers.

In what way does any number or mathematical principle exist?

-jon

 

[Philip]

In what way does any number or mathematical principle exist?

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 $pi$.

 

[jon1101]

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 $pi$.

this is from http://citd.scar.utoronto.ca/CITDPress/holtorf/3.8.html

"Radical Constructivism puts forward two main claims (Glasersfeld 1989: 162):

'(a) knowledge is not passively received but actively built up by the cognizing subject;
(b) the function of cognition is adaptive and serves the organization of the experiential world, not the discovery of ontological reality.'"

Now, I do not claim to be an expert on constructivism, and thus I apologize if I am misinterpreting this quote or if this quote is not representative of what you mean by "constructivism," but given this, I contend that pi, for instance, serves in the organization of the experiential world, due to the simple fact that pi is useful. Circles and spheres exist, and pi helps to organize their existence in mathematical terms.

-jon