Cool number stuff

[morondog]

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

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

[houseofcantor]

137, which kinda looks like this thingy:



only upside down.

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

[morondog]

(12-12-2011 03:16 AM)houseofcantor Wrote:  666 is triangular, like 6:

That's absolutely delightful 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.

[houseofcantor]

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?

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.

Then the three,

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.

[morondog]

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

Please tell me this is cool and not just nerdy

[aurora]

(12-12-2011 03:16 AM)houseofcantor Wrote:  137, which kinda looks like this thingy:



only upside down.

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

HoC, you totally freak me out, sometimes (in a good way)

[houseofcantor]

(12-12-2011 04:14 AM)morondog Wrote:  Please tell me this is cool and not just nerdy

But if this nerd calls it cool, then what?

[morondog]

(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

But if this nerd calls it cool, then what?

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

[houseofcantor]

(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

But if this nerd calls it cool, then what?

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

It's totally square, man.

[cufflink]

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:



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 . . .



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.