Cool number stuff
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12-12-2011, 02:34 AM
Cool number stuff
So ja...

When I was young, I have no idea where my knowledge of this fact came from originally, but

666 = 36 + 35 + ... + 1

Here's the cool thing: you don't have to actually do all the adding up.

36 + 35 + ... + 1
1 + 2 + ... + 36
----------------------
37 + 37 + ... + 37 <-- this 37 gets added up 36 times

So 36 x 37 = 2 x (36 + 35 + ... + 1)

And 36 x 37 / 2 = 36 + 35 + ... + 1

So 18 x 37 = 36 + 35 + ... + 1

Now 18 = 20 - 2 and 37 = 40 - 3 so
18 x 37 = (20 - 2) x (40 - 3) = 20 x 40 - 2 x 40 - 3 x 20 + 6 = 800 - 80 - 60 + 6
= 666

You can see you can apply this method to any number. Try 10 + 9 + ... + 1 Wink

Anyone else got any fun number facts ? I enjoy collecting nuggets like this and I guess quite a few people have such things squirreled away in their minds Smile
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12-12-2011, 03:16 AM
RE: Cool number stuff
137, which kinda looks like this thingy:

[Image: 8a685fb411de0b0a1f1663cd66b432a0.png]

only upside down. Tongue

I'm too geeky for this topic. 666 is triangular, like 6:
Heart
HeartHeart
HeartHeartHeart

[Image: 10289811_592837817482059_8815379025397103823_n.jpg]
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12-12-2011, 03:20 AM (This post was last modified: 12-12-2011 03:30 AM by morondog.)
RE: Cool number stuff
(12-12-2011 03:16 AM)houseofcantor Wrote:  666 is triangular, like 6:
Heart
HeartHeart
HeartHeartHeart

That's absolutely delightful Smile I didn't know that...
Here's another thing:

If a number is divisible by 3, then the sum of its digits is divisible by 3. Same for 9. So:

70,914,357

7 + 9 + 1 + 4 + 3 + 5 + 7 = 36

3 + 6 = 9

so 70,914,357 is divisible by 9.
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12-12-2011, 03:39 AM
RE: Cool number stuff
Number of the beast is technically 616 if you go by the oldest account. 616 makes more sense; but when has it ever been about sense with Christians and their numerology? Tongue

My number is 4, of course; and a cool sequence is the code, g c a t comme ca: 7/3/1/20. Buncha weirdness with that set in that order. Wink

HeartHeart
HeartHeartHeart
HeartHeart
Then the three,
Heart
HeartHeart
But if you play with the numbers and the patterns, you can see some shenanigans. Like how 6 was a Jew number, and the Christians adopted the 7 to get one over on them; 7 being the male number of completeness...

Like I said, too geeky for this topic. Big Grin

[Image: 10289811_592837817482059_8815379025397103823_n.jpg]
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12-12-2011, 04:14 AM
RE: Cool number stuff
To find the highest common factor of two numbers, it's easy using the Euclidean algorithm:

Start say with 132 and 84
132 / 84 = 1 with remainder 48

Then
84 / 48 = 1 with remainder 36

48 / 36 = 1 with remainder 12

36 / 12 = 0 so 12 is the highest common factor of 132 and 84 Smile

Please tell me this is cool and not just nerdy Tongue
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12-12-2011, 04:18 AM
RE: Cool number stuff
(12-12-2011 03:16 AM)houseofcantor Wrote:  137, which kinda looks like this thingy:

[Image: 8a685fb411de0b0a1f1663cd66b432a0.png]

only upside down. Tongue

I'm too geeky for this topic. 666 is triangular, like 6:
Heart
HeartHeart
HeartHeartHeart

HoC, you totally freak me out, sometimes (in a good way) Wink
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12-12-2011, 04:19 AM
RE: Cool number stuff
(12-12-2011 04:14 AM)morondog Wrote:  Please tell me this is cool and not just nerdy Tongue

But if this nerd calls it cool, then what? Big Grin

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12-12-2011, 04:47 AM
RE: Cool number stuff
(12-12-2011 04:19 AM)houseofcantor Wrote:  
(12-12-2011 04:14 AM)morondog Wrote:  Please tell me this is cool and not just nerdy Tongue

But if this nerd calls it cool, then what? Big Grin

Oh fuck I think I need to become a Christian. Nerd hell I cannot face...
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12-12-2011, 05:34 AM
RE: Cool number stuff
(12-12-2011 04:47 AM)morondog Wrote:  
(12-12-2011 04:19 AM)houseofcantor Wrote:  
(12-12-2011 04:14 AM)morondog Wrote:  Please tell me this is cool and not just nerdy Tongue

But if this nerd calls it cool, then what? Big Grin

Oh fuck I think I need to become a Christian. Nerd hell I cannot face...

It's totally square, man.

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13-12-2011, 01:13 AM
RE: Cool number stuff
I've always found certain infinite series very cool. This one is a favorite:

Take the fractions with 1 in the numerator: 1/1, 1/2, 1/3, 1/4, 1/5, . . .

Square each one . . .

and add them up. That is:

[Image: 792989f06227ee20a55269219408c7fc.png]

Obviously you can't add all of them, because there's an infinite number. But the further you go, the closer you get to a definite value. That value is approximately 1.644934, which doesn't look particularly interesting, until you find out that it's actually . . .

[Image: 66d516864963a2587bb840a2a0ab4fe1.png]

Pi squared over 6! It's amazing to me how pi gets involved with things that have nothing to do with circles and diameters.

The result was discovered by Euler in 1735.

Religious disputes are like arguments in a madhouse over which inmate really is Napoleon.
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