The ideal number.

For the discussion of math. Duh.

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neoliminal
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The ideal number.

Postby neoliminal » Tue Dec 29, 2009 6:07 pm UTC

Someone was saying that 10 was the ideal number in the main comic thread (bemoaning the number of planets being 8). Noted was that 9 has a square root of 3, while 12 is very pleasing in different base systems.

So what is your ideal number and why?
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Re: The ideal number.

Postby Tirian » Tue Dec 29, 2009 7:40 pm UTC

Ideal for what?

Not waiting for the answer, I'll go ahead and say that six is an under-appreciated number. It's easy to multiply numbers in base-six, and it's easy to count off on one hand. (I've never quite understood why people think that your base has to be based on the number of fingers that you have instead of one more.) In addition, it's within ordinary human mental capacity to remember and differentiate between six things, so its natural to have six main characters in a television show or breaking a problem into six pieces.

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Re: The ideal number.

Postby jroelofs » Tue Dec 29, 2009 9:28 pm UTC

Six is also cool because: 1+2+3 = 6 = 1*2*3.

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Re: The ideal number.

Postby doogly » Tue Dec 29, 2009 9:41 pm UTC

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Re: The ideal number.

Postby Talith » Tue Dec 29, 2009 10:38 pm UTC

I've always been partial to 64. I think it stems from my noting that it was a square and a cube before the fact was brought up in class. It's the same reason that I like multiplying numbers by 9, because I found a pretty quick method before it was taught to us.

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Re: The ideal number.

Postby t0rajir0u » Wed Dec 30, 2009 12:27 am UTC


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Dason
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Re: The ideal number.

Postby Dason » Wed Dec 30, 2009 12:58 am UTC

42. Need I say more?
double epsilon = -.0000001;

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Re: The ideal number.

Postby Shivari » Wed Dec 30, 2009 1:56 am UTC

Talith wrote:I've always been partial to 64.


ME TOO! =D

(No idea why, though)

It's the same reason that I like multiplying numbers by 9, because I found a pretty quick method before it was taught to us.


Is it the 9 times x is just whatever the higher 10 is minus x? (e.g. 9 x 6 = 54 = 60 - 6) That trick made multiplying by 9 way more intuitive in 5th grade.

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Re: The ideal number.

Postby Charlie! » Wed Dec 30, 2009 8:05 am UTC

42.
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Re: The ideal number.

Postby Quigibo » Wed Dec 30, 2009 9:06 am UTC

3711251

Its ideal if you convert it to base 26 with alphanumerics (with 'a' being zero)
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Re: The ideal number.

Postby Flightless_bird » Wed Dec 30, 2009 10:11 am UTC

I like 27. Mostly because I like 3 and 27 is 3^3
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Re: The ideal number.

Postby thicknavyrain » Wed Dec 30, 2009 10:48 am UTC

ThickNavyRain in the "Number war" thread wrote:I chose 6!
Many of the measurements of time are in multiples of 6 (60 seconds, 60 min, 24 hours)
6 is also a perfect number (multiples = 1, 2, 3. 1+2+3=6)
Only number that is both the sum and the product of three consecutive whole numbers (1,2,3)
It's a highly composite number
It's a triangular number as is it's square (36).
6 Rules. (12 does to, but you can consider it what 20 is to 10 in base 6).
I love 6.
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Re: The ideal number.

Postby minno » Wed Dec 30, 2009 4:04 pm UTC

I like 2520, since all numbers up to 10 are its factors. A lot of my first programming experience was making programs to compute factors of numbers.
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Re: The ideal number.

Postby gorcee » Wed Dec 30, 2009 4:12 pm UTC

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

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Re: The ideal number.

Postby TheWaterBear » Wed Dec 30, 2009 4:56 pm UTC

t0rajir0u wrote:24.


I thought I was the only one! 24 ftw!

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Re: The ideal number.

Postby Turtlewing » Wed Dec 30, 2009 6:19 pm UTC

I'm fond of 26, mostly because it has some history in an PRG group i was in during high school (White Star 26 was a recuring ship, even in settings not associated with Babylon 5). I think it was also the name of the little dinosaur in the Dinotopia miniseries.

As for bases, i like base 8, because it converts intuitively to binary and doesn't require more digets than you're used to (unkile hexidecimal).

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Re: The ideal number.

Postby Macbi » Wed Dec 30, 2009 6:42 pm UTC

At the moment I think 71 and 77 are pretty cool, because they don't look interesting but have connections to the Look-and-Say sequence and Egyptian primes respectively.
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Re: The ideal number.

Postby mr-mitch » Wed Dec 30, 2009 7:31 pm UTC

6 is also cool because the volume and surface area of a cube with sides of length 6 units are both 216 units(squared or cubed).

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Re: The ideal number.

Postby PM 2Ring » Thu Dec 31, 2009 1:01 pm UTC

Talith wrote:I've always been partial to 64. I think it stems from my noting that it was a square and a cube before the fact was brought up in class. It's the same reason that I like multiplying numbers by 9, because I found a pretty quick method before it was taught to us.

Me, too. But then I learned about the index laws & factorization, and realize that this nice property of 64 was just another manifestation of the awesomeness of 6. :)

And here's some more 6 awesomeness:
Image

Golomb ruler of order 4 and length 6. This ruler is both optimal and perfect.

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Re: The ideal number.

Postby Kurushimi » Thu Dec 31, 2009 2:49 pm UTC

I think I need to make some remarks about 3.

Have you heard about the scale riddle? You have 8 balls, and all of them weigh the same except one, which is heavier than all the rest. Your job is to find the heavy ball with the least amount of weighings. Many people assume you need 3 weighings to do this, but you can do it in 2. In fact, with n balls, instead of log_2 n tries, it takes log_3 n tries to do it.

Also, every number can be represented as the sum and difference of unique powers of 3.

1 = 1
2 = 3 - 1
3 = 3
4 = 3+ 1
5 = 9 - 3 - 1
6 = 9 - 3
7 = 9 - 3 + 1

And so on. I'm also pretty sure 3 is the only number with that property.

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Re: The ideal number.

Postby Certhas » Thu Dec 31, 2009 3:13 pm UTC

4 = 2+2 = 2*2 = 2^2
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Re: The ideal number.

Postby Xanthir » Thu Dec 31, 2009 4:46 pm UTC

Certhas wrote:4 = 2+2 = 2*2 = 2^2

It also equal 2^^2, 2^(3)2, and all higher tetrations.
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Re: The ideal number.

Postby PM 2Ring » Thu Dec 31, 2009 5:11 pm UTC

For every property of the natural numbers, there must be a smallest number with that property. And since there are a lot more interesting properties than there are small numbers, plenty of small numbers turn out to be interesting for multiple reasons, 2 being a fairly notorious example. :)

http://en.wikipedia.org/wiki/Strong_Law_of_Small_Numbers wrote:"The Strong Law of Small Numbers" is a humorous paper by mathematician Richard K. Guy and also the so-called law that it proclaims: "There aren't enough small numbers to meet the many demands made of them."[1] In other words, any given small number appears in far more contexts than may seem reasonable, leading to many apparently surprising coincidences in mathematics, simply because small numbers appear so often and yet are so few.


Another nice property of 10:
(1²+1) (2²+1) = (3²+1) = 10

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Re: The ideal number.

Postby Yakk » Thu Dec 31, 2009 7:34 pm UTC

My favourite prime is 91.
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Re: The ideal number.

Postby Tirian » Thu Dec 31, 2009 9:38 pm UTC

Yakk wrote:My favourite prime is 91.


It's certainly pretty cool that it the largest prime that is divisible by 7.

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Re: The ideal number.

Postby skeptical scientist » Thu Dec 31, 2009 9:43 pm UTC

I think Yakk's point is that it is, iirc, the only number under 100 which passes the easy tests for compositeness - divisibility by 2, 3, and 5 (which are the easiest divisibility tests in base 10), divisibility by 11 (which is easy for numbers under 100), and being a perfect square - and yet fails to be prime.
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Re: The ideal number.

Postby ceaser13 » Fri Jan 01, 2010 12:44 am UTC

Image

Call it the romantic in me.
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Re: The ideal number.

Postby Osha » Fri Jan 01, 2010 4:58 am UTC

Take a disk image of Boom Blox Bash Party
Convert it to a (very long) integer.
Tada.

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Re: The ideal number.

Postby PM 2Ring » Fri Jan 01, 2010 6:08 am UTC

Osha wrote:Take a disk image of Boom Blox Bash Party
Convert it to a (very long) integer.
Tada.

Nice try, Osha, but in this thread we're only interested in the intrinsic properties of the number, not those that derive from its representation in some arbitrary base.

:)

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Re: The ideal number.

Postby Kurushimi » Fri Jan 01, 2010 3:44 pm UTC

Nobody post! There are 28 replies in this topic. It's perfect!

Wait, darn.

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Re: The ideal number.

Postby minno » Fri Jan 01, 2010 5:01 pm UTC

Kurushimi wrote:Nobody post! There are 28 replies in this topic. It's perfect!

Wait, darn.


OK, now we stop at 30.
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Re: The ideal number.

Postby squareroot1 » Sun Jan 03, 2010 12:35 am UTC

But 30 isn't prime.

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Re: The ideal number.

Postby Kurushimi » Sun Jan 03, 2010 1:44 am UTC

Neither is 32.

But it is a power 2.

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Re: The ideal number.

Postby Macbi » Sun Jan 03, 2010 10:17 am UTC

As it turns out the "replies" column in the fora counts the amount of replies, not the amount of posts, so we now have 34 posts.
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Re: The ideal number.

Postby Kurushimi » Sun Jan 03, 2010 2:58 pm UTC

Who said anything about posts? We were talking about replies.

Another numbers I enjoy are 32768, 65536, 2147483648, and 4294967296.

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Re: The ideal number.

Postby PM 2Ring » Mon Jan 04, 2010 12:19 pm UTC

squareroot1 wrote:But 30 isn't prime.
But it is primorial. And all composites <=30 share a common factor with 30.

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Re: The ideal number.

Postby Quaternia » Mon Jan 04, 2010 6:48 pm UTC

2.
It's more the fear factor: every time I do something in number theory, I always offer thanks that it's the only even prime number :mrgreen:
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Re: The ideal number.

Postby mrcheesypants » Mon Jan 04, 2010 10:30 pm UTC

No love for 1?
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Re: The ideal number.

Postby DarkRat » Mon Jan 04, 2010 11:58 pm UTC

423

has 42 and 23 in it

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Re: The ideal number.

Postby doogly » Tue Jan 05, 2010 12:02 am UTC

mrcheesypants wrote:No love for 1?

One is the loneliest number.
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