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#3576 Re: Help Me ! » Is there a definition of an integer? » 2006-01-21 20:17:35

R = [2sin((90n - 180)/n) / sin(360/n)] - 1

The problem with a rational test is that 1.1 / 2.4 is rational.  That's 11 / 24.  And there's even more problems with that.  Values such as 1.1 can not be stored entirely in binary.  You can get close, but not exact.  So you can't tell the difference between 1.1 and 1.1000000000000001.  And further more, irrational numbers can't be stored on the computer anyways.  You can have an approximation, but that's it.

I'll think more on this problem tonight, but I believe it can not be solved through a computer.

#3577 Re: Help Me ! » Is there a definition of an integer? » 2006-01-21 20:06:01

A rounding function should be relativly easy to write, though.

float y;
int x = y + 0.5;

Here are my functions >smile
y = 1
y = |x| / x
y = sqrt(x^2)

Those are not natural numbers.

You want a cool function?  Take the binary value stored in a float, and save that value in an unsigned integer.  This can easily be done with pointers:

#include <iostream>

using namespace std;

int main()
{
    float *f = new float;
    *f = -5.3;
    cout << *((unsigned int *)f) << endl;

    delete f;
}

The output is:  3232340378

The thing that's cool about this function is that (on a computer) it's 1-1 and onto.  Of course, in real life it's not because there are a greater amount of fractions (rationals) than there are integers.

#3578 Re: Help Me ! » Find two numbers from a single number » 2006-01-21 14:37:20

Maybe I didn't explain it well.  Have your function be the summation of perfect squares:

f(17) = 16 + 1
f(29) = 25 + 4
f(25) = 9 + 16

#3579 Re: Help Me ! » Find two numbers from a single number » 2006-01-21 06:01:03

Scratch that, summation of primes isn't 1-1.  11+5 = 16 and 13 + 3 = 16.  How about summation of perfect squares?

Oh, and I just realized, there is no function f(a, b) that could be 1-1 and onto if the size of the less than the size of the domain squared.  This is because there are a*b ways to put a and b together, but if the range isn't that size (which is your case here), there is no way for it to be 1-1.

#3580 Re: Help Me ! » Find two numbers from a single number » 2006-01-21 05:58:59

Sounds like cryptography.  I can't understand however, why the last number could be 256.  That isn't in the extended ascii, nor could it be held by a character (in computers).

You want a function that is one to one.   What this means is that:

if f(a, b) = f(c, d) then a=c and b=d

Now you don't say that this function has to use all of it's range.  That is, for every b in the result (the range) of the function, there is a y that gives you it:

For all b in Range, there exists an a in Domain such that f(a) = b.

This is called onto.

One such function that is 1-1 (one to one) but isn't onto is summation of primes:

f(a, b) = a + b, where a and b are primes.

I believe this is 1-1, but I don't think I can prove it.  However, this is fairly hard to get the original values a and b out when you are given a number such as 12.

#3581 Re: Help Me ! » Sines » 2006-01-20 10:18:00

y = Asin(ωt + Φ)

There is a fourth constant you can use:

y = Asin(ωt + Φ) + C

It doens't mean anything when talking about scientific waves (such as modeling sound), but it can be used to help make the sin graph go through a certain point.

#3582 Re: Help Me ! » Graeme » 2006-01-20 08:18:40

It's called senior year in America.  Of course, unlike high school, being an actual senior doesn't mean you get to beat up on the juniors.

#3583 Re: Help Me ! » Calculating Odds » 2006-01-19 14:45:16

Depends how you define a 3 digit number.  Is 001 a three digit number?

Assuming that it isn't, 100 is the smallest three digit number.  100 + 100 + 100 = 300 is the smallest sum of three digit numbers.  999 + 999 + 999 = 2997.  All other numbers inbetween these two are also valid.  That is, the range of answers is [300, 2997].  This means the number of possible answers is 2997 - 300 = 2697.  When you take 1 guess, you have a 1/2697 chance of getting it right.

#3584 Re: Maths Is Fun - Suggestions and Comments » Help! (Might be a little pathetic to ask actually) » 2006-01-19 14:10:22

gmail is google mail.  It has the most storage space of any free email on the internet, and also adds a variety of features.  One of my favorite is search.  In gmail, you don't store your mail in folders, although you certainly can.  Instead, you search for.  You can search by date, author, subject, content, or anything else you can think of.

Another favorite of mine is auto save.  When typing a new email, gmail auto saves it for you ever minute.  If you accidentally close your browser while typing, it will still be there.

For a partial list of features, go to: http://mail.google.com/mail/help/about_whatsnew.html

If you want to get gmail, you have to be invited.  If you want me to invite you, send me an email at rshadarack@hotmail.com

Don't post your email here, web crawlers will see it and companies that spam will get it.  The only reason why I can is that is my junk email address.

#3586 Re: Help Me ! » Calculating Irregular Areas » 2006-01-19 02:21:19

You have to decompose the figure.  For example, if it's a triangle on top of a square, first find the area of the square, then the area of the triangle, and add them together.

#3587 Re: Help Me ! » A tricky problem to get you all thinking... » 2006-01-18 15:38:05

"Pi isn't random, and neither, I presume, are sudoku grids."

It is random, but only once.

If you think of each digit of pi as a number, you cannot predict the next number by knowing the one you have.  That is part of the definition of random.

Of course, the second part of that is that it can't repeat when starting over, which pi doesn't.

Now it's more complex than this.  Many people think there are patterns in the digits of pi.  For example, a lot think that 9 will drop out at some point completely.  This is still under current study.

But let's just rephrase the question.  If there 1,241,100,000,000 numbers in a row, what's the chance of it being a sudoku grid, when layed out left to right, top to bottom?

This is fairly complex because when you look at the grid starting off at the first digit, it is mostly the same as the grid starting off at the second digit.  If the first digit contains an invalid number (like 99) at the very end, then so will the second, and the third, and the fourth, and so on.

#3588 Re: Help Me ! » 2 Event Probobility » 2006-01-18 15:30:36

Your teacher is wrong.

"A printer printed a card with black ink on blue paper and an envelope with blue ink on blue paper."

If it was "or", then it would be 1/21.

Explain it like this:

The chance of event A happening is 1/42, and the change of event B happening is 1/42.  Are you telling me that the chances of both of them happening is greater than the chance of just a single one?  Doesn't that sound wrong?

#3589 This is Cool » Irrationality of sqrt(n) » 2006-01-18 11:21:25

Ricky
Replies: 2

For a math class, advanced calculus, a homework assignment was to show that the √5 is irrational.  I took it a step further.  I first tried looking a proof for it up on the web, but it I couldn't find any that didn't have serious errors which made the whole attempt invalid.  Let me know if you find any errors in this.

Hmm, doesn't seem to let me upload pdf's.  Oh well:

http://www.geocities.com/rshadarack/sqr … tional.pdf

Oh, and it's odd for two reasons: the general proof is just as short as that for √2, and it uses a completely different strategy.

#3590 Re: Help Me ! » Extrema » 2006-01-17 14:07:18

why would i get a crit # but no max or min

It would be a saddle point.  The slope of the graph is 0 at that point, but it is not a local max or min.  For example, x^3 has a saddle point at (0,0).

#3591 Re: Help Me ! » diffrentiation » 2006-01-17 14:04:53

I think it does since you have to plug in and multiply less.

#3593 Re: Help Me ! » diffrentiation » 2006-01-17 13:30:20

Now, if you don't have access to a calculator, try to assume that x+1 is a factor.  If that doesn't work, try to assume x+2 is a factor.  Because if has any other factors, you don't really care about them.

If you know polynomial division, you can use this too.

#3594 Re: Help Me ! » diffrentiation » 2006-01-17 13:22:10

Ti-89 to the rescue!

2(x+1)(x+2)(2x+3)

#3595 Re: Maths Is Fun - Suggestions and Comments » Getting rid of SchwanzerIsBack » 2006-01-17 10:52:05

He can always create another account though..

Unless you ban him through ip, in which case, if he is computer savy enough, he can change.

#3596 Maths Is Fun - Suggestions and Comments » Getting rid of SchwanzerIsBack » 2006-01-17 09:42:10

Ricky
Replies: 5

http://news.com.com/Create+an+e-annoyance%2C+go+to+jail/2010-1028_3-6022491.html?part=rss&tag=6022491&subj=news

Trolling, especially posting nudity on a forum, is now illegal.  What I suggest is to get SchwanzerIsBack's ip address, and either threaten to notify the authorities, or actually notify them.  Through this, they can subpoena his service provider to give his address.

#3597 Re: Help Me ! » Partial diffrentiation » 2006-01-17 09:27:13

ƒ(x,y) = e^2xy^2 cos(3y)

You need to use parenthesis.  is it e^(2), e^(2x), etc...

Assuming it's e^(2x) * y^2 * cos(3y):

¶f/¶x:

Assume that y is a constant.  So y^2*cos(3y) is a constant.  Let y^2*cos(3y) = k.  The equation then becomes:

k*e^(2x)

Taking the derivative, this is: 2ke^(2x), which is 2(y^2*cos(3y))*e^(2x).

Now try the same for y.

#3598 Re: Help Me ! » Very interesting problems.. » 2006-01-17 04:25:03

Got my program down to 0.371 seconds when doing 2-32 by calculating where the next perfect root will be instead of linearly searching for it.

#3599 Re: Maths Is Fun - Suggestions and Comments » Help! (Might be a little pathetic to ask actually) » 2006-01-17 03:20:30

gmail is the way to go.  +2 gigabytes of space.   You need to be invited to it though.

#3600 Re: Jokes » "Classic" Joke » 2006-01-17 03:15:35

Why were there more people buying products from the company called "Bad" than the company called "Good"?

Both were sued for false advertising.

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