Count by meaningful numbers

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12obin
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Count by meaningful numbers

Postby 12obin » Sat Oct 18, 2014 6:53 am UTC

I'll give two examples because it's easier to demonstrate than just explain.
Sweet 16
365 days in a year

Count upward by numbers with which you associate some meaning. It can be a personal meaning for you, too. And it can take a sentence or so to explain if needed.
You can skip numbers, but try not to skip too far at once, and give people some time to respond before you add a post where you're skipping. You can also post non-integers if you have one.
No back-tracking. You can only post a number higher than the previous post.
For the two examples I gave above, you can use my examples because I kind of ruined them.
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Vytron
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Re: Count by meaningful numbers

Postby Vytron » Sat Oct 18, 2014 7:47 am UTC

-1/12

My favorite number because I find intriguing how there are people in the world that think it's the result of the set {1 + 2 + 3 + 4... (up to infinity)}

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bachaddict
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Re: Count by meaningful numbers

Postby bachaddict » Sat Oct 18, 2014 7:28 pm UTC

Not part of the game now, and I see there are many meaningful numbers that can go before it.
Spoiler:
√2 - Equals about 1.414, a very interesting and useful number.

It is interesting because it is the diagonal of a square side one. It is irrational, meaning that if you graph y=x*√2, the only graph point the line passes through is 0,0. I remember this graph because it was illustrated by a square standing up diagonally at x=1, with its top corner giving the point for the graph line at y=√2.

It's used in ISO 216 paper sizes, meaning the aspect ratio stays the same when the paper is cut in half.
Last edited by bachaddict on Sun Oct 19, 2014 5:30 am UTC, edited 1 time in total.
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12obin
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Re: Count by meaningful numbers

Postby 12obin » Sat Oct 18, 2014 7:52 pm UTC

Can you briefly explain what's interesting about it, or even just give a link? The spirit of the game/activity is sort of that everyone should understand why a number is on the list.
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Vytron
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Re: Count by meaningful numbers

Postby Vytron » Sat Oct 18, 2014 11:34 pm UTC

I agree with 12obin.

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Reecer6
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Re: Count by meaningful numbers

Postby Reecer6 » Sat Oct 18, 2014 11:49 pm UTC

While we wait for an answer, let's make it non-canon.

One is important because it's the single only value in the English language that makes you not pluralize a noun.

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Vytron
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Re: Count by meaningful numbers

Postby Vytron » Sun Oct 19, 2014 1:37 am UTC

1.059463094359295264561825294946

Which is the twelfth root of two (that is, if you multiply it by itself 12 times you get 2.)

It's the proportion between the frequencies of adjacent semitones in the equal temperament scale.

It's important because without it we wouldn't be able to tune the difference in the musical notes of virtual instruments (for real instruments we can do it by ear - with this number we can pick any kind of sound, and make a virtual instrument out of it by just separating every note by a factor of 1.059463094359295264561825294946.)

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12obin
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Re: Count by meaningful numbers

Postby 12obin » Sun Oct 19, 2014 2:49 am UTC

Reecer6 wrote:While we wait for an answer, let's make it non-canon.


That's okay. They can just edit the existing post if they want.
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Vytron
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Re: Count by meaningful numbers

Postby Vytron » Sun Oct 19, 2014 3:43 am UTC

I don't know if this is legal, but I don't see in the rules mentioning that it's illegal to count when someone else has posted after you if they didn't keep counting.

1.060660171779821286601266543157

Which is the Square Root of 2 multiplied by 3 and divided by 4.

Why is it interesting:

Imagine a cube that has all the sides being length 1. Now, imagine that there's another cube that passes through this cube and makes a hole through it. It turns out, that if the new cube is too big, the old cube is destroyed. So there's a cube with a size that is the biggest one that can pass through the old cube without destroying it. The biggest cube is called a Prince Rupert's Cube, and has all the sides being length 1.060660171779821286601266543157.

After the hole is made the cube of length one looks like this:

Image

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Adam H
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Re: Count by meaningful numbers

Postby Adam H » Mon Oct 20, 2014 3:35 pm UTC

1.1

It's the first palindrome.

Or, if you are a pedant, it's the first palindrome that isn't stupid (like 0.0 or 1) or messed up by the decimal point or negative sign (like .505 or -1.1) or what have you.
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Re: Count by meaningful numbers

Postby Sean Quixote » Mon Oct 20, 2014 6:26 pm UTC

√2 ≈ 1.41421356237309504880168872420969807856967187537694807317667973799 ...

Ratio of the length of the hypotenuse to the legs of a right isosceles triangle. Probably the oldest-known irrational number.

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Vytron
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Re: Count by meaningful numbers

Postby Vytron » Mon Oct 20, 2014 8:40 pm UTC

I guess I was just too slow to come with a convincing explanation for this, so ignore this message.

Spoiler:
1.080604612

This number has no actual significance or importance in the number line, but by the end of this post I'll promise you'll find it interesting too.

So let's talk first, about complex numbers.

But first we need to talk about imaginary numbers.

What happened is that mathematicians didn't have enough fun with real numbers, because, there's an infinite uncountable number of them from 0 to 1, and from any integer to another. But once you've proved that you can't list them all, you're done.

Now that you know and can give a name to every single point in the number line, where do you go? Well, what about making up numbers that currently don't exist? The first such number is this one:

i

You won't find this number in this thread, or in any other counting thread.

This is because this number is not on the number line, no operation between numbers on the number line produces this number.

Is that so? Well, not really.

It turns out that if you ask for the square root of -1, you get this guy.

i*i=-1

0 connects the number line with the line of imaginary numbers, which runs vertically to it.

So i is actually 1i, and there's also 0.5i, the square root of -0.5, and googol plexi, the square root of negative googol plex, and so on.

This imaginary number line is vertical, and if you go down you move towards negative imaginary infinity, and if you go up you move towards imaginary infinity (the square root of negative infinity.)

That's simple enough, imaginary number behave just like real numbers. But now you can't make operations between real and imaginary numbers.

Is that so? Well, not really.

What happens is, just like getting the square root of -1 doesn't get you back to the number line, operations between the real and imaginary number lines don't land you back on either line.

So, what happens if you sum i and 1? Well, you don't get 1i, that'd be i+0. What you do is you take a look at the plane, where both lines intersect, and you draw a vertical line coming from the 1, and draw a horizontal line coming from i. When they intersect you get your result, and it looks like this:

i + 1 = 1 + i

And you may say "well, we got nowhere!"

Except we did.

1+i is a complex number! The + there doesn't mean "sum 1 + i", it's actually part of the name of the 1+i value in the so called complex plane. The complex plane contains all the possible results of operations between the number line and the imaginary number line.

But that's not enough to make 1.080604612 interesting, for that, we also need another number, which is:

e

This is a real number named after some random guy named Euler.

It's the limit of (1+(1/n))^n, as n approaches infinity, and it's about 2.71828.

The interesting thing about 1.080604612 is that there's two ways to arrive at this number. The first one is to just do:

Take the cosine of 1 and multiply it by 2:

2cos(1)=1.080604612

The second one is to take e, and square it by itself i times to get a.

And take e, and square it by itself negative i times to get b.

And then sum a and b.

e^i = 0.540302306 + 0.841470985 i

e^-1 = 0.540302306 - 0.841470985 i

The 0.841470985s cancel out each other and you end with:

a=0.540302306
b=0.540302306

0.540302306*2=

1.080604612

Wasn't that interesting?

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bachaddict
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Re: Count by meaningful numbers

Postby bachaddict » Tue Oct 21, 2014 1:17 am UTC

1.618...
Spoiler:
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042180176696349133695996064322005328873494893135966030424380804565944743335678
31672703729636367594216999379522
The Golden Ratio.
Image
a and b are in the golden ratio if a+b:a=a:b

This ratio is found in nature and pretty much everywhere else.
slinches wrote:Also, the OTC isn't a disease. In fact, it's the cure. As we all know, Time heals all wounds.

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Re: Count by meaningful numbers

Postby Vytron » Tue Oct 21, 2014 1:37 am UTC

1.6325269

Sorry to crop it at 7 significant digits.

Anyway, this is the square root of 2 multiplied by itself square root of 2 times.

It's important because it's used to prove that an irrational number to an irrational power may be rational.

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Re: Count by meaningful numbers

Postby 12obin » Tue Oct 21, 2014 1:53 am UTC

I should have predicted that it would go all mathy like this.
I'm kind of into it but I totally didn't anticipate it.
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Re: Count by meaningful numbers

Postby Sean Quixote » Tue Oct 21, 2014 4:31 am UTC

2

Smallest and only even prime number. Largest number that's the factorial of itself (and for that matter, the number of numbers that are the factorial of themselves :P). The essence of duality. The number of thumbs that "this guy" usually possesses.

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Re: Count by meaningful numbers

Postby bachaddict » Tue Oct 21, 2014 4:41 am UTC

2.71828...

Euler's Constant. Much, much weirder than π. Used in compound interest and other, nerdier things.
12obin wrote:I should have predicted that it would go all mathy like this.
I'm kind of into it but I totally didn't anticipate it.

We've got to get all the little interesting numbers out of the way before we can get on to personally significant ones!
EDIT: I hope I'm not spoiling Vytron's game of counting up in the smallest possible steps.
slinches wrote:Also, the OTC isn't a disease. In fact, it's the cure. As we all know, Time heals all wounds.

Thanks for the molpish wig ggh!
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Re: Count by meaningful numbers

Postby 12obin » Tue Oct 21, 2014 6:23 am UTC

Oh dammit I missed 2 because I was letting you get all your deep math things out. I'm getting 3 before someone gets in ahead of me, and then I think I know what will come next.

3 is a number that has a School House Rock song about it. It is also significant for the structural integrity of triangles.
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Re: Count by meaningful numbers

Postby Vytron » Tue Oct 21, 2014 10:18 pm UTC

12obin wrote:I think I know what will come next.


You do?

3.031088913245535263673031097632

This is the square root of 3, divided by 4 (multiplied by 7.)

It's the Area of an equilateral triangle with side length 7.

bachaddict wrote:EDIT: I hope I'm not spoiling Vytron's game of counting up in the smallest possible steps.


Don't worry, I'll manage :mrgreen:

I now wonder if the next guy will skip to 4 XD

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Re: Count by meaningful numbers

Postby Sean Quixote » Wed Oct 22, 2014 12:50 am UTC

22/7

Approximation of π, sufficient for "most" practical calculations. Okay, I have a feeling I probably shouldn't say most, lest I betray my ignorance. Slightly larger, though, so, yes I am a troll. :twisted:

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Re: Count by meaningful numbers

Postby Vytron » Wed Oct 22, 2014 2:26 am UTC

I still don't get why people use that symbol for pi when there's a much better one available (𝜋.) Seriously, every time people have to use a symbol they use π. I'd certainly would never use π if I had to draw pi on a blackboard.

Back to topic:

3.162277660168379331998893544433

This is the square root of 10.

It's the result of the square root of 2 multiplied by the square root of 5 (the area of a rectangle with those sides.)

The length of the diagonal of a rectangle of sides 1 and 3.

The length of the diagonal of a rectangle of sides 2 and the square root of 6.

The length of the diagonal of a rectangle of sides square root of 3 and the square root of 7.

And the length of the diagonal of a square with sides square root of 5.

It's cool because this is like the pi of 4 sided shapes!

Spoiler:
Or, if you divide the area of a 4 sided shape by the square root of 10 you get the pi of 4 sided shapes, leave me alone!

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Re: Count by meaningful numbers

Postby Sean Quixote » Wed Oct 22, 2014 3:31 am UTC

Well, at least one reason not to use it here is that apparently this forum isn't compatible with whichever Unicode thingy (there I go displaying my ignorance again) that it's a part of... *shrug*

Anyway, this isn't a counting post I just absolutely had to say that for whatever reason. :P

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Re: Count by meaningful numbers

Postby Vytron » Wed Oct 22, 2014 7:39 am UTC

Sean Quixote wrote: this forum isn't compatible with whichever Unicode thingy (there I go displaying my ignorance again) that it's a part of...


Wait, what? Do you see a box with numbers or a question mark instead of pi there?

Anyway, continuing:

γ

AKA 3.275822918721811159787681882 (Lévy's constant)

Which is e (Euler's Constant as mentioned by bachaddict) multiplied by itself 1.1865691104 times.

1.1865691104 is 𝜋 squared and divided by 12*0.693147181

0.693147181 is ln 2.

ln 2 means "the natural logarithm of 2".

What is a natural logarithm? Well, to understand them you have to understand numeric bases.

In this thread we all use base 10, base 10 means, that we use 10 symbols to represent numbers, those symbols are:

0 1 2 3 4 5 6 7 8 9

And once you run out of symbols, you use again your first and second symbol to represent the next value:

10

And so on.

There's also base 1:

1 11 111 1111 11111...

Binary, the language of computers:

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111...

Hexadecimal, used by computers to group binary numbers:

0 1 2 3 4 5 6 7 8 9 A B C D F

The dozenal system, superior to the decimal system that we use, because it has very nice looking values for which decimal has the crappy 0.333repeating/0.666repeating stuff:

0 1 2 3 4 5 6 7 8 9 𝓧 Ɛ

Anyway, a natural logarithm is that number written in base e (Euler's Constant as mentioned by bachaddict), or a number base with e symbols.

γ is important because that's to where all (except finitely many) real numbers arrive if you take the limit of (xn)^1/n as n approaches infinity.

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Re: Count by meaningful numbers

Postby Adam H » Wed Oct 22, 2014 3:13 pm UTC

5.

I have 5 fingers on each hand and 5 toes on each feet.
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Re: Count by meaningful numbers

Postby brenok » Wed Oct 22, 2014 6:08 pm UTC

7

The colors of the rainbow, the capital sins, the ancient wonders etc.

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Re: Count by meaningful numbers

Postby Vytron » Wed Oct 22, 2014 9:05 pm UTC

7.03467422498391652049818601859902130

Which is the result of the Lambert W function for 1/2, multiplied by 20.

Which is the inverse of the function:

f(n)=n*(e^n)

(where e is Euler's Constant as mentioned by bachaddict, and n is any number)

This is actually a very useful function in science:

  • It's used in Planck's law, which describes the electromagnetic radiation emitted by a black body in thermal equilibrium at a definite temperature.
  • It's used in Bose–Einstein statistics and Fermi–Dirac statistics, which in quantum statistics, is one of two possible ways in which a collection of non-interacting indistinguishable particles may occupy a set of available discrete energy states, at thermodynamic equilibrium, and describes a distribution of particles in certain systems comprising many identical particles that obey the Pauli exclusion principle, respectively.
  • Occurs in the results of delay differential equations, in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times.
  • In the Michaelis–Menten kinetics of enzyme kinetics of biochemistry, describes a closed-form solution for the time course kinetics analysis.

I have no idea what any of that means, but I'm pretty sure that's very important!

This number in embedded in nature!

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Re: Count by meaningful numbers

Postby phillip1882 » Fri Oct 24, 2014 4:49 am UTC

8.5397342226735670654635508695466
pi*e. enough said.
good luck have fun

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Re: Count by meaningful numbers

Postby Vytron » Fri Oct 24, 2014 5:51 am UTC

^Um, well, so I'll assume a meaning number multiplied by another meaningful number is also meaningful.

8.66025403784438646763723170753

The square root of 3 divided by 2.

Altitude of an equilateral triangle with side length 10.

It's meaningful because, to know the altitude of any equilateral triangle, all you need to do is multiply the length of one of the sides by this number, and then divide by 10.

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Re: Count by meaningful numbers

Postby bachaddict » Fri Oct 24, 2014 8:12 am UTC

9.
It's meaningful because nine of an object can be arranged into a 3x3 grid with the same aspect ratio as the original object. Works best with squares.
It's the highest digit in base 10. When working with computers you get used to numbering things from 0-9 rather than 1-10.
Personally meaningful because it features twice in my birth year :)
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Re: Count by meaningful numbers

Postby Vytron » Fri Oct 24, 2014 10:10 pm UTC

9.06472028365438761924

This is 𝜋 divided by the natural logarithm of 2 (ln(2)) multiplied by 2.

In the Van der Pauw method, it's used to calculating sheet resistance (by using nested intervals that converge slowly but steadily to Rs = R*9.06472028365438761924/2) and 9.06472028365438761924/2 it's known as Van der Pauw's constant.

It's important because it allows us to measure of resistance of thin films that are nominally uniform in thickness. It is commonly used to characterize materials made by semiconductor doping, metal deposition, resistive paste printing, and glass coating.

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Re: Count by meaningful numbers

Postby 12obin » Sat Oct 25, 2014 6:21 am UTC

10 is the total number of hand digits on most humans/ primates. This is evolutionarily significant wrt tool use, and also is the basis of our commonly used decimal number system.
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Re: Count by meaningful numbers

Postby Vytron » Sat Oct 25, 2014 8:02 am UTC

^But, if you check the video I posted before, that's only because the French made it so, and it's their fault we have to use 2 hands to count to 10 (when 1 hand is enough to count to 12). We might be a better mathematical world if it weren't for the French Revolution (specifically, many people "are bad at math" due to the difficulty added by the decimal system, so we'd have more people being good at it if we taught children a different system that is easier to use).

But why am I ranting here? o_O Er, back to topic. Good to see you contributing 12obin.

L

This is Landau's constant L, a number that we really don't know exactly, but it's a value between

10 < L*20 < 10.88

That is, it could be, for all we know, 10.000...big number of 0s...0001 (when multiplied by 20.)

Why is it important?

Well, let's go back to the complex plane. You know that when we talk about the number 1, we can imagine a line that goes from to 0 to 1:

Code: Select all

.-------.
0       1


Well, on the imaginary numbers, we can draw a line that goes from 0 to i.

Code: Select all

.i
¦
¦
¦
.0


So what happens when you draw a circle, that touches these points, and has 0 at its center? We have what is called an "unit disk." A disk that is plotted which has radius 1, and from its center, the outline of the circle is at distance 1 from the center.

This is easy for the complex plane because it's a 2D object and you can only take a direction in 360 degrees or its fractions. But what happens when you take other kind of planes that are stretched or squeezed out? Imagine that you have an elastic page of paper, and that you stretch and squeeze it in some way, and then, you draw on it, the complex plane, and you draw a circle of length 1 as described above.

Once you let it go, you'd have a very deformed circle on your deformed plane, and now the distances from the outline of your circle to the center of the plane would vary.

Holomorphic functions are used to differentiate and analyze the many ways in where, say, you could stretch the elastic page and the many planes that you could have in it.

A biholomorphic function is a function that allows you to translate an image that you draw in some plane to another plane.

What Landau did was defining F to be the set of all holomorphic functions for which a given function on the unit disk gives you 1 with an input of 0, L_f would be the radius of the largest disk in f, and B_f would be the radius of the largest disk in a biholomorphic image of a subset of a unit disk (that is, a piece of the disk that can be translated into the function to give a value of 1 with an input of 0.)

Finally, we have to talk about infimums and supremums in mathematics.

Suppose you have a set that has, I don't know, all the positive numbers that are even and below 100, these would be:

2, 4, 6...96, 98

So in this set, you can create a new subset, composed of numbers multiple of 4. And you have this new set:

4, 8, 12...92, 96.

So in this set, the infimum is the lowest value (4), and the supremum is the highest value (96)

What Landau found out was that the infimum of the set of all possible values in L_f or B_f were his three constants:

8.66 + (20x10^-14) < B*20 < 9.44

10 < A*20 < 15.706

And our little friend.

10 < L*20 < 10.88

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Re: Count by meaningful numbers

Postby 12obin » Sun Oct 26, 2014 2:04 am UTC

11 is the age I was the first time I menstruated, but then it went away again until like two years later.
Robin, she.

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Vytron
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Re: Count by meaningful numbers

Postby Vytron » Sun Oct 26, 2014 6:15 am UTC

11.0001...

No, huh, I kinda like, can't do this this time around, images of 12obin I can't get out of my head, too distracting...

So, instead, I'll go with:

12

It is meaningful because it's the two first digits of the name of the creator of this thread, who menstruated for the first time when E* was 11, but then it went away again until like two years later.

*) E, the ultimate gender neutral pronoun I just made up, not to be confused by Euler's Constant as mentioned by bachaddict.

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Re: Count by meaningful numbers

Postby 12obin » Sun Oct 26, 2014 7:35 am UTC

(i.e. it is a sequence of numbers that resembles a capital letter R)
Robin, she.

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Vytron
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Re: Count by meaningful numbers

Postby Vytron » Sun Oct 26, 2014 8:26 am UTC

(I think the 1 is unnecessary, would work the same for me if it was just 2obin:

Image

Or something)

2edundant
Spoiler:
2obin.png
2obin.png (14.61 KiB) Viewed 6677 times

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12obin
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Re: Count by meaningful numbers

Postby 12obin » Sun Oct 26, 2014 7:27 pm UTC

(Tru. But I also use twelveobin in other places. Which I like better than twoobin.)

13
The number of people at The Last Supper in Christian tradition. Commonly seen as an unlucky number in Christian and Christian-influenced cultures.
Robin, she.

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patzer
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Re: Count by meaningful numbers

Postby patzer » Sun Oct 26, 2014 8:47 pm UTC

15.15426224147926...

This is ee.

It's interesting because if one plots a graph of x^y=y^x, for non-negative real values of x and y, two lines will appear. A straight line where x=y, and a curved line passing through points such as (4,2) and (2,4). The two lines cross at the point (e,e).

(Random piece of trivia I discovered when doodling on graph paper as a little math-obsessed child)
If it looks like a duck, and quacks like a duck, we have at least to consider the possibility that we have a small aquatic bird of the family Anatidae on our hands. –Douglas Adams

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Vytron
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Re: Count by meaningful numbers

Postby Vytron » Sun Oct 26, 2014 11:37 pm UTC

(twelveobin sounds funny)

15.284473071784413259813974625

This is the Landau–Ramanujan constant (multiplied by 20)

Suppose you have a big number, called x. They found out that there's a number of integers less than x which are the sum of two square numbers.

The number of integers can be found by the formula:

x divided by square root of natural logarithm of x.

The constant appears when you define N(x) as the number of positive integers less than x that are the sum of two squares. Then you see what you get when you plug it into the formula:

(N(x) multiplied by square root of natural logarithm of x) divided by x

And see its limit as x approaches infinity.

You get:

15.284473071784413259813974625 divided by 20.

This is meaningful because what this means is, if you want to know how many integers there are below some number n that are the sum of two squares, all you need to do is multiply your number by 15.284473071784413259813974625 and divide by 20, and you'll get an approximation (the approximation will get better the bigger your number.)

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Re: Count by meaningful numbers

Postby phillip1882 » Thu Oct 30, 2014 2:56 am UTC

16.
2^4
4^2. very cool little property. the only value where i can get it two different ways with x^y and x != y.
good luck have fun


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