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Benford's Law

Take a big pile of really random numbers.

If they are truly random, the first digit in each number will NOT be randomly distributed from 1-9. In fact, about 30% of the time, the first digit will be 1.

The number 2 will be the first digit a little over 17% of the time, and the probability drops and drops until you get to 9, which is the first digit only about 4.5% of the time.

This is used by the IRS in forensic accounting and fraud detection.

Truly random data showing extremely predictable behaviour? Fucking awesome.

If you plot natural numbers in a spiral grid, the primes start to appear in diagonals.

WTF, Ulam?

stewie wrote:Benford's Law

Take a big pile of really random numbers.

If they are truly random, the first digit in each number will NOT be randomly distributed from 1-9. In fact, about 30% of the time, the first digit will be 1.

The number 2 will be the first digit a little over 17% of the time, and the probability drops and drops until you get to 9, which is the first digit only about 4.5% of the time.

This is used by the IRS in forensic accounting and fraud detection.

Truly random data showing extremely predictable behaviour? Fucking awesome.

So that's why my iPod plays three Tiny Tim songs in a row.

Add any single digit number to the number 9 and the the resulting digits in the sum added to each another are the same as the original single digit number.

Ex:

7+9= 16
1+6= 7

4+9= 13
1+3= 4

The same holds true with double digit numbers, though they have to be reduced to a single digit number first.

Ex:

44*+9= 53
[*where 4+4= 8]
5+3= 8

25*+9= 34
[*where 2+5=7]
3+4= 7

If you do the same thing with multiplication, the end result will always be 9.

Ex:

4*9= 36
3+6= 9

50*9= 450
4+5+0= 9

465*9= 4185
4+1+8+5= 18
1+8= 9

um...i suck at math.

I've seen a special case of one of Gauss' many things in the user description things... but e^(i*x) = cos(x) + i*sin(x)... where
e is Euler's number, the base of the natural logarithm, 2.718... you know
i is the "square root of negative 1"
x is an angle, in radians (2*pi of those in a circle, as opposed to 360 degrees in a circle. Really handy unit for math and physics and electronics)
^ is exponentiation (2^3 = 2*2*2, for example)

Use x = pi. The sine of pi is zero, and the cosine of pi is -1. Hence, e^(i*pi)=-1. It all seems very abstract (how do you multiply a number by itself an imaginary number of times? Let alone pi times?) but it's really really nice to work with instead of trig, and the special case is often mentioned as the most beautiful expression in math, for bringing a whole lot of seemingly totally unconnected mathematical concepts together.

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Can anybody give me a concise description of Ramsey Number Theory?

steve wrote:Can anybody give me a concise description of Ramsey Number Theory?

Have you read this?

Is this to determine how many players must be seated at the table to be sure there'll be at least one fish?

I still think the multiples of nine finger trick is really awesome. It's still quite HANDY for those who are mathematically incompetent.

I'm assuming everyone already knows it so I won't bother trying to explain...