The ideal number.

For the discussion of math. Duh.

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Flightless_bird
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Re: The ideal number.

Postby Flightless_bird » Tue Jan 05, 2010 10:36 am UTC

doogly wrote:
mrcheesypants wrote:No love for 1?

One is the loneliest number.

Two can be as bad as one.
Trying is the first step towards failure

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Re: The ideal number.

Postby TheWaterBear » Tue Jan 05, 2010 10:35 pm UTC


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olubunmi
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Re: The ideal number.

Postby olubunmi » Thu Jan 07, 2010 7:17 pm UTC

31

Because I really like the 31 Equal temperament

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Re: The ideal number.

Postby PM 2Ring » Fri Jan 08, 2010 1:47 am UTC

olubunmi wrote:31

Because I really like the 31 Equal temperament


I prefer 53 note equal temperament; it tends to be more accurate. It'd be a bit unwieldy on traditional instruments, but it's ok on a computer.


But my favourite number today is 51. Although I'm generally unimpressed by properties relating to the representation of numbers in some base, occasionally I make exceptions. Just check out the patterns in the decimal expansion of sqrt(51):

7.141428428542849997999399811...

Notice that the first 5 digits after the decimal point are the same as the first 5 digits of sqrt(2), and it also has the 1428 pattern from the decimal of 1/7. But my favourite feature is the two close groups of 999 that arise rather early in the decimal expansion.

Its continued fraction contains just 7 & 14: sqrt(51) = 7 + 1/(7 + 1/(14 + 1/(7 + 1/(14 + ...))))

For more digits see

http://www2.research.att.com/~njas/sequences/A010504

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Re: The ideal number.

Postby DarkRat » Fri Jan 08, 2010 2:46 pm UTC

Flightless_bird wrote:
doogly wrote:
mrcheesypants wrote:No love for 1?

One is the loneliest number.

Two can be as bad as one.

It's the loneliest number, since the number one


scrn

tuttamarie
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Re: The ideal number.

Postby tuttamarie » Sun Jan 10, 2010 4:46 pm UTC

I like 2 because it's the only even prime

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Re: The ideal number.

Postby olubunmi » Sun Jan 10, 2010 4:52 pm UTC

PM 2Ring wrote:
olubunmi wrote:31

Because I really like the 31 Equal temperament


I prefer 53 note equal temperament; it tends to be more accurate. It'd be a bit unwieldy on traditional instruments, but it's ok on a computer.




And I prefer 31 because it's doable to build instruments with it. Believe me when I say this sounds great :D

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Re: The ideal number.

Postby gmalivuk » Sun Jan 10, 2010 7:44 pm UTC

tuttamarie wrote:I like 2 because it's the only even prime

And 3 is the only prime divisible by 3, and 5 is the only prime divisible by 5...
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Re: The ideal number.

Postby thicknavyrain » Sun Jan 10, 2010 9:27 pm UTC

gmalivuk wrote:
tuttamarie wrote:I like 2 because it's the only even prime

And 3 is the only prime divisible by 3, and 5 is the only prime divisible by 5...


Those primes are all snooty bastards.

"Oooh, I'm only divisible by MYSELF and one, but that's ok because s/he was here before all of us. Except 0...but nobody likes her..."
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Re: The ideal number.

Postby polymer » Sun Jan 10, 2010 10:01 pm UTC

I think 0 is awfully fun. Any other number can be seen as "big", or "small" as you want since the scale is arbitrary, except zero. It's always just zero no matter how you scale the system...

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Re: The ideal number.

Postby stephentyrone » Mon Jan 11, 2010 12:09 am UTC

olubunmi wrote:
PM 2Ring wrote:
olubunmi wrote:31
Because I really like the 31 Equal temperament

I prefer 53 note equal temperament; it tends to be more accurate. It'd be a bit unwieldy on traditional instruments, but it's ok on a computer.

And I prefer 31 because it's doable to build instruments with it. Believe me when I say this sounds great :D

19-tet kicks both 53- and 31-tet's asses so hard that it's not funny. Not only can you build instruments in 19-tet, but you can write music in 19-tet with only a modest adaption of notation, and you still get those beautiful thirds.
I think 0 is awfully fun. Any other number can be seen as "big", or "small" as you want since the scale is arbitrary, except zero. It's always just zero no matter how you scale the system...

Only if you're not interested in multiplicative structure.
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Re: The ideal number.

Postby Kurushimi » Mon Jan 11, 2010 1:20 am UTC

gmalivuk wrote:
tuttamarie wrote:I like 2 because it's the only even prime

And 3 is the only prime divisible by 3, and 5 is the only prime divisible by 5...


I thought the same exact thing.

I don't much care for 220, or 284 on their own, but together they form one cool pair.

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Re: The ideal number.

Postby eggdudeguy » Mon Jan 11, 2010 1:58 am UTC

The people who said 42 are provably correct.
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Re: The ideal number.

Postby Dason » Mon Jan 11, 2010 2:05 pm UTC

eggdudeguy wrote:The people who said 42 are provably correct.

Now this is one smart dude. Probably has a phd because he's definitely a practicing awesomematologist.
double epsilon = -.0000001;

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Re: The ideal number.

Postby Niall » Mon Jan 11, 2010 3:44 pm UTC

Seven is kind of a loose cannon. All the other numbers know to keep their distance. I was at a Christmas function once and seven ate nine.

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Re: The ideal number.

Postby Syrin » Mon Jan 11, 2010 4:09 pm UTC

I'm rather fond of 808017424794512875886459904961710757005754368000000000, myself.

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Re: The ideal number.

Postby Indon » Mon Jan 11, 2010 6:28 pm UTC

gmalivuk wrote:And 3 is the only prime divisible by 3, and 5 is the only prime divisible by 5...


2 is also the most common (non-1) factor found among the natural numbers, for fairly obvious reasons.

I'm a fan of the factorials, myself, due to the divisibility properties. Is there a term for the series of numbers which would be the products of the series of primes? (2, 6, 30, 210, 2310, etc) I think I'd like those a little bit more.
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Re: The ideal number.

Postby Talith » Mon Jan 11, 2010 6:36 pm UTC

Indon wrote:
gmalivuk wrote:And 3 is the only prime divisible by 3, and 5 is the only prime divisible by 5...


2 is also the most common (non-1) factor found among the natural numbers, for fairly obvious reasons.

I'm a fan of the factorials, myself, due to the divisibility properties. Is there a term for the series of numbers which would be the products of the series of primes? (2, 6, 30, 210, 2310, etc) I think I'd like those a little bit more.

OEIS: A002110

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Re: The ideal number.

Postby Kurushimi » Mon Jan 11, 2010 9:22 pm UTC

Why is 1 in that list?

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Re: The ideal number.

Postby Ended » Mon Jan 11, 2010 9:35 pm UTC

Kurushimi wrote:Why is 1 in that list?

The offset of the sequence is 0, meaning that the first term is the "product of first 0 primes". This is an empty product and by convention equals 1 (similar to how an empty sum equals 0).
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Re: The ideal number.

Postby eggdudeguy » Mon Jan 11, 2010 11:38 pm UTC

Dason wrote:
eggdudeguy wrote:The people who said 42 are provably correct.

Now this is one smart dude. Probably has a phd because he's definitely a practicing awesomematologist.

Yeah!
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Re: The ideal number.

Postby Kurushimi » Tue Jan 12, 2010 1:29 am UTC

Ended wrote:
Kurushimi wrote:Why is 1 in that list?

The offset of the sequence is 0, meaning that the first term is the "product of first 0 primes". This is an empty product and by convention equals 1 (similar to how an empty sum equals 0).


Ah, I always took the empty product to be 0. If I remember working on something recently where this caused some confusion. I think that would make more sense.

Question, what would be the empty exponentiation?

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Re: The ideal number.

Postby PM 2Ring » Tue Jan 12, 2010 4:14 am UTC

I always took the empty product to be 0.
Not a good plan if you ever want your products to grow. :)

Question, what would be the empty exponentiation?
Also 1. Just think about the index laws.

Also note that 0 factorial = 1 since it's also the empty product.

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Re: The ideal number.

Postby squareroot1 » Tue Jan 12, 2010 11:30 pm UTC

Syrin wrote:I'm rather fond of 808017424794512875886459904961710757005754368000000000, myself.

Is that 45! ? Or maybe 46!,47!,48! or 49! ?

I don't particularly want to check.
Last edited by squareroot1 on Tue Jan 12, 2010 11:36 pm UTC, edited 1 time in total.

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Re: The ideal number.

Postby Dason » Tue Jan 12, 2010 11:33 pm UTC

squareroot1 wrote:
Syrin wrote:I'm rather fond of 808017424794512875886459904961710757005754368000000000, myself.

Is that 30! ? Or maybe 31!,32!,33! or 34! ?

I don't particularly want to check.

http://www.wolframalpha.com/input/?i=808017424794512875886459904961710757005754368000000000
It appears that Syrin is fond of it because it's the order of the monster group.
double epsilon = -.0000001;

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Re: The ideal number.

Postby squareroot1 » Tue Jan 12, 2010 11:38 pm UTC

Oh right, the order of the Monster group. I've seen that before; I feel so silly for forgetting.

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Re: The ideal number.

Postby Raptortech97 » Mon Jan 18, 2010 5:13 pm UTC

I'm fond of **************************************************************************** and ****************************************************************** because they're my RSA keys.
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Re: The ideal number.

Postby DavCrav » Mon Jan 18, 2010 9:19 pm UTC

Syrin wrote:I'm rather fond of 808017424794512875886459904961710757005754368000000000, myself.


I was ninja'd, but as soon as I saw this I wanted to say 'that's a monstrous number'. I thank you.

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Re: The ideal number.

Postby illiriks » Tue Jan 19, 2010 1:15 am UTC

60. 1, 2, 3, 4, 5, 6, 10, 15, 20, and 30 are factors, making it a highly composite number. 60Hz is a frequency that can interfere with the human heart. Most LCD monitors and older TVs run at 60Hz. The first fullerene molecule discovered had 60 carbon atoms per molecule. 60 is the sum of twin primes (29 + 31), the sum of four consecutive primes (11 + 13 + 17 + 19), and between two primes itself (59 and 61). 'Nuff said.

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Re: The ideal number.

Postby snowyowl » Sat Jan 23, 2010 5:20 pm UTC

As long as I don't have to actually use it for anything, I'm gonna say my pet number is 1729.
1729=123+13=103+93
Most useless property of any integer*, but still quite endearing.

(*Well, other than the fact that there are 4 letters in the word "four".)
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Re: The ideal number.

Postby Suffusion of Yellow » Tue Jan 26, 2010 2:53 am UTC

e.

gorcee wrote:64 is my lucky number, for a variety of reasons.


Are they "you like music and dislike Kennedy?"


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