## Wednesday, August 19, 2009

### What is the most interesting number ?

What are the most interesting numbers- I allow reals and complex numbers this time. To avoid having too many numbers I have restricted it to numbers that have had entire books written about them (there is one exception that I note below), and to be of mathematical interest (e.g., the speed of light is not included and the square root of 2, which I did include, perhaps shouldn't have been).

Review of books on 0,1,pi, e: here, Review of a book on i: here. Review of a book on square root of 2: here. Review of a book on phi: here. Review of a book on gamma (whats gamma?): here. If there is some mathematical constant that has had a book on it that I have not included, please comment.

Here is my choice ranked in order of how important they are.
1. 0. Addition is more basic then multiplication so the additive identity comes before the multiplicative identity.
2. 1. Multiplicative identity.
3. -1. Negative numbers--- what would we do without them? One could even argue that subtraction is more important than multiplication and make this number 2 on the list. There is no book on -1 that I know of, but it is still too important to not put on this list.
4. pi. Without pi we wouldn't have circles!
5. e. Ah-ha- the pi vs. e debate. You can read about it here or even listen to a real debate here. I would go with pi since the level of math it is on is more basic then the level of math that e is on.
6. gamma. What is this constant? It is the difference in the limit between natural log of n and 1 + 1/2 + ... + 1/n. How important is it? I read the book on it pointed to above. The book is pretty good but it mostly talks about related topics- logs, Zeta functions, pi. So I still don't see why gamma is worth a book. I suspect that there are more math constants that are more important that just happened to not have books written about them. Or they have and I don't know about them.
7. phi. There is the notion that the Golden Ratio pops up in math and in nature all the time. And there are those who disagree.
8. square root of 2. This is interesting historically as the first irrational number, but I don't think it has much mathematical significance.

1. This book contains information on many interesting constants. Of course the ones GASARCH lists above are the first ones treated in Finch's book.

2. I would put the number "2" on the list in position 5.5, after e and before phi.

(1) Where would we be without binary, i.e. 2ary, operators such as "+" and "*"?
(2) The constant 2 shows up disproportionately, often indirectly as "even" and "odd".
(3) It's the first prime.

3. What number is i?

4. i is the complex number such that i^2=-1.

5. not the but a complex number such that i^2=-1. Otherwise, i=-i.

6. I meant "What position on the list is i?".

7. As Harrison said in the last post, 24 is a very interesting number. There's even a whole TV show about it. =)

8. WHOOPS- I meant to put i
after e, but this can all be debated, as we are doing.

bill g.

9. As Harrison said in the last post, 24 is a very interesting number. There's even a whole TV show about it. =)

Go leech lattice, go!

http://en.wikipedia.org/wiki/Leech_lattice

10. Omega is an interesting number that has a book written about it (MetaMath):

http://en.wikipedia.org/wiki/Chaitin%27s_constant

11. What happened to the pi versus 2pi debate? No one is going to claim that 2pi is the most interesting number?

12. I meant to put i after e

I thought that "i" comes before "e" except when it sounds like "a" as in "neighbor" and "weigh"

13. I can't stand the term 'complex numbers'.

We don't refer to the elements of other fields as 'numbers'.

14. The oracle to the halting problem...

...with its digits alternating with those of pi. (Throw in countably many more numbers if you like.)

15. What about Chaitin's Omega? He practically wrote a whole book about it.

16. Chaitin is too much in love with himself for anything he says to be taken seriously.

17. What about the very large number 337736875876935471466319632506024463200.00000080231935662524957710441240659. It can be found at OEIS A161771, http://www.research.att.com/~njas/sequences/A161771

It involves the 24d space of the Leech Lattice and a square term of 'Ramunujan constant'. It has many interesting properties.