The ideal number.

For the discussion of math. Duh.

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Flightless_bird
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Re: The ideal number.

doogly wrote:
mrcheesypants wrote:No love for 1?

One is the loneliest number.

Two can be as bad as one.
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TheWaterBear
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Re: The ideal number.

olubunmi
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Re: The ideal number.

31

Because I really like the 31 Equal temperament

PM 2Ring
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Re: The ideal number.

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

DarkRat
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Re: The ideal number.

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.

I like 2 because it's the only even prime

olubunmi
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Re: The ideal number.

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

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Re: The ideal number.

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.

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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polymer
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Re: The ideal number.

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.

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

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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Kurushimi
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Re: The ideal number.

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.

eggdudeguy
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Re: The ideal number.

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

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;

Niall
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Re: The ideal number.

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.

Syrin
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Re: The ideal number.

I'm rather fond of 808017424794512875886459904961710757005754368000000000, myself.

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Re: The ideal number.

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.

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

Kurushimi
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Re: The ideal number.

Why is 1 in that list?

Ended
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Re: The ideal number.

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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eggdudeguy
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Re: The ideal number.

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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Kurushimi
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Re: The ideal number.

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?

PM 2Ring
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Re: The ideal number.

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.

squareroot1
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Re: The ideal number.

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.

Dason
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Re: The ideal number.

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;

squareroot1
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Re: The ideal number.

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

Raptortech97
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Re: The ideal number.

I'm fond of **************************************************************************** and ****************************************************************** because they're my RSA keys.

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DavCrav
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Re: The ideal number.

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.

illiriks
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Re: The ideal number.

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.

snowyowl
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Re: The ideal number.

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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Suffusion of Yellow
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Re: The ideal number.

e.

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

Are they "you like music and dislike Kennedy?"