The cool numbers thread.
 

OK. To start it off, and give credit, I read this book by french author Bernard Werber(who obvioulsy did not find this info himself, but w/e).
This is an interesting random cool number I found in it.
142 857 (or, for americans...142,857)

let's start by multiplying this number by 1, 2, 3, 4, 5, and 6....
142 857 x 1 = 142 857 ....(obvioulsy)
142 857 x 2 = 285 714
142 857 x 3 = 428 571 (hmm..)
142 857 x 4 = 571 428 (hmmmmmmmmmmm.....)
142 857 x 5 = 714 285
142 857 x 6 = 857 142
OK. To those of you who haven't noticed, the results have exactly the same numbers, but it seems the order has been shifted each time...cool right??
But wait. It's not over...
142 857 x 7?
.
.
.
999 999!!! Strange, huh?....
especially when..
142 + 857 = 999
and, oh wait...
14 + 28 + 57 = 99
142 857 square, or 142 857^2 = 20408122449
and 20408 + 122449 = 142 857
cool right? :crazy:

Actually, it is. I always sucked at math, but this is fun :D

Very cool. I always wonder when I see numbers like this if there is some secret to the nature of things that might be useful in predicting the stock market, etc.. kinda like in "Pi, the Movie".

Wow, that's really interesting! The sheer concidence, or is it? Hmm...
Thanks for sharing, I probably never would have known this otherwise. I can only guess at the amount of research that went into it.

Is there any other number with similar properties? Is there a name for such a number?

/reminds myself to read this up.

I'll try to look for some other cool numbers, I have stumbled across some other ones, but none with an many cool things as this one.

dont forget E^pi*i = 1

[thats "e" euler's number, raised to the power of the product 'pi' and 'i']

equals one.
strange..

That is really cool. Math has a lot of cool stuff going on, if you can get past the boring parts.

Actually, 142,857 x 9 = 1,285,713...

thanks man, I meant 142,857 x 7

Learned it a long time ago (you might have seen it before)
98765432 / 8 = 12345679
(it is supposed to be done on the old calculators that you can only put 8 nubers in)

All numbers are "cool numbers."

Proof:

1. Assume that not all numbers are cool.

2. Divide the numbers into the set of cool numbers and the set of
not-cool numbers.

3. Now, consider the set of not-cool numbers. One of them is less than
all of the others, which means it is the lowest not-cool number in the
universe! Hey, that's pretty cool. Move it to the cool number set.

4. Repeat step 3 until the not-cool set is empty. This means that all
numbers are cool, QED.

A book that you be interested in is "Curious and Interesting Numbers" by David Wells.
It has a whole load of numbers, all put in numerical order, so its almost like a number dictionary.

Opening it at random i find things such as:

371 = 3³ + 7³ + 1³

12,321 = 111², also 1,234,321 = 1111², etc.


3,628,800
Equal to 10! and the only factorial that is the product of other consecutive factorials (apart from the trivial ones involving 1!).
10! = 6! * 7!

10! also equals 3! * 5! * 7!.

These examples are all very short, but some of the explainations go on for paragraphs or even pages (esp. pi, e, phi, etc.).

Interesting book, but not exactly cover to cover reading!

To prove: 0.9 repeating = 1

[proof follows below]

1. let x = 0.9 repeating
2. multiply each side by ten, giving

10x = 9.9 repeating

3. subtract x from the left, 0.9 repeating
from the right, giving

9x = 9

4. divide both by nine, giving

x = 1

5. yet x = 0.9 repeating
6. therefore

0.9 repeating = 1

ehh, I didn't relize there was a thread on this. I apologize for my ignorance.

Haha. That's quite...cool.
Did you think that up yourself?

Dim memory tells me it showed up in an ancient
Martin Gardner column in Scientific American —
originally phrased as a proof that there are no
"uninteresting" numbers.

The coolest number of all of course is "42".

For those of you for whom this makes no sense, I refer you to "The Hitch-hiker's Guide to the Galaxy" by the late Douglas Adams.

e^(Pi*i)=-1 not 1.

Your partition results in infinite unbounded sets either upper or lower, so point 3 is not true.

9 is probably the most interesting number i know.

Aye! that's a most interesting read!! i strongly recommend it to anyone. It's actually a trilogy in four parts. Excellent stuff.

daking dont be a smartass! :p

Heheh yea im sorry was in a bad mood last nite Monitor broke :(. My appologies

The original post is indeed interesting, but it is also mere coincidence. Let me state a couple reasons:

1) Everything done to the number is dependent that it is base 10. Numbers, by definition, are base-less, and we use bases simply to express them. This means that there is most probably a number in every other base that fits this property, but is also probably not the same number.

2) If I came up with a number of random properties that would be "cool" I could use simple algebra and/or my computer to find a number that fit those properties, then post it around the internet as if it were a neat find. Is it really that cool, though? Not really very useful, if you ask me.

Sorry if this ruined the mood of the post. As I said, I think it's a pretty neat number, but from a mathematics theory standpoint, not a very useful find.

Cool number ideed, saw this somewere recently.

Same type of thing...

10101010 x 10101010 = 10203040

What it really equals is 102030403020100.

-Mikey

damn freaky
i allways hated maths.....................but now.................nup i still do

but its still freaky

Cheers

5 parts actualy.

Math... at least it's good for something! j/k

-BD

The number 9 is pretty cool actually.

9 multiply by anything, then adding that number up give you back a 9. Quite neat isn't it.

Eg. 9 x 3 = 27
2 + 7 = 9

This one is relatively easy to explain - it will work for all 1-based numbers. Consider 11:
Every 1-based number is results in the same type of thing - just adding the number times the various factors of 10, and then sum. ie
11*11 = 11*1 + 11*10 = 121
111*111 = 111*1 + 111*10 + 111*100 = 12321

Not particularly scientific, but...
take a calculator key-pad. any 3 digit number pattern added to the pattern "reflected" through the centre of the keypad gives the same answer, 1110.

For example, 789 + 123, 654 + 456, 147 + 963
Slightly more interesting: 748 + 362

Any number theorists in our midst? I'm sure they come across things like this pretty often...once you get into multidimensional sets things get fun and pretty to graph :)