Basics - Digest

Some challenges for the programmers out there

Sun, 22 Nov 2009 20:20:49 GMT

Basics : Some challenges for the programmers out there

Quote:

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

If you want to have a crack at the problems then follow the link below:
http://projecteuler.net/index.php?section=problems

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Need help catching up on my physics.

Thu, 19 Nov 2009 12:25:57 GMT

Basics : Need help catching up on my physics.

So, I just missed about a week and a half of school due to H1N1 , and my Physics teacher isn't the best at explaining things to begin with...

That being said, I missed pretty much everything on forces, how to draw free-body diagrams, what each of the forces are etc. He tried to explain it to me when I asked him, but it wasn't the best of explanations.

Also, when I came back, they had started doing stuff on momentum 2 days beforehand. I kind of understand this stuff, but I'm slightly confused on a few things. The problems we've been doing are like m1v1 + m2v2 = ......
Something like that, I don't have any of my papers in front of me right now so, I'm not really sure what the rest of the equation is offhand.

But yeah , I missed a couple assignments which he wants in by Monday.

So if someone can explain forces and momentum to me , or even give me some sort of resources, that would be greatly appreciated, seeing as my teacher's explanations aren't the best.

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Stats : 2 Replies

Can anyone prove that 1 plus 1 equals 2?

Thu, 12 Nov 2009 13:52:50 GMT

Basics : Can anyone prove that 1 plus 1 equals 2?

Yes, I know, it sounds crazy, but I'm serious:

Can anyone prove that 1 plus 1 equals 2?

infinisa wrote:

biljap wrote:

Ahh I will never forget my first class, where we got a long and confusing proof that one plus one equals two

Really? I'm impressed! I never saw such a proof at school, but once read a book (in German!) in which this result was proudly presented as theorem no. 50!

Good luck to you all!

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Stats : 6 Replies

moving Lift or Not

Fri, 06 Nov 2009 08:19:31 GMT

Basics : moving Lift or Not

Hi ,

Suppose you are in a closed lift. You dont know whether it is moving.

How will you understand that if the lift is:

1.

Moving down uniformily

or
2.

Moving Up unifirmily

or
3.

Lift is at rest

The commen thing in above three cases is that
we do not feel any change in weight in our body.

Then how will you find motion status of the lift

Please Share your ideas

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Stats : 5 Replies

A Math problem:Points in a 3D space (Quite hard)

Mon, 02 Nov 2009 04:37:42 GMT

Basics : A Math problem:Points in a 3D space (Quite hard)

Ok so I mastered some maths but I have a genuine problem that if anyone can give me some real insight I would be genuinely pleased.

First here are the minimum requirements before you even attempt this (If your still reading we'll begin)

(1)An understanding of 3D spaces described by x, y, z coordinates (So that you could describe where a flying insect was located in the room). The room has a height of X a width of Y and a depth of Z.
(2)A grasp of Trigonometry and Pythagoras

The problem:
(1)You have a

circular flat surface

in the room (as described above) but it is not even with the floor (Actually it can be at quite an angle).
(2)The

centre of the flat surface is a known height from the floor

(3)You have

2 other points

on the circular flat surface where the height from the floor

is also known

and the distance from them to the centre is also known.
(4)At any point someone comes into the room and fixes a very thin pole on to the uneven (to the floor) circular flat surface.

The pole touches the centre of the circular flat surface

and extends outwards past the edge and as its length is known.
(5)Assume the pole has no diameter but you can still see it.

How do you calculate the height of the end of the thin pole from the floor?

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Stats : 7 Replies

Is time travel possible in future

Sun, 01 Nov 2009 20:29:02 GMT

Basics : Is time travel possible in future

I read a book with the following review of it
In this fascinating book, the renowned astrophysicist J. Richard Gott leads time travel out of the world of H. G. Wells and into the realm of scientific possibility. Building on theories posited by Einstein and advanced.
What do you guys think is it possible to travel in time

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Stats : 70 Replies

why is letter e so important?

Fri, 30 Oct 2009 22:11:28 GMT

Basics : why is letter e so important?

We know e is defined as e= lim(x->0)(1+x)^(1/x).
Why is e often used as base while taking log, though it's exact value is not known like pi?

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Stats : 12 Replies

Math tricky 9

Fri, 30 Oct 2009 08:37:10 GMT

Basics : Math tricky 9

Hai I have some cool trick with 9 !

step1.

Immagine a number between 1 and 9 (single digit)

step2.

multilpy that number with 9

step3.

If the result contain ONLY 1 digit continue to step 4. If result have 2 digits in it ADD the two digit

step4.

now add 1 to it

step5.

YOUR ANSWER IS

, hOW IS IT...

COMMENT PLEASE

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Stats : 25 Replies

physics - flash

Tue, 27 Oct 2009 14:16:41 GMT

Basics : physics - flash

hypothetical, if I swim in a lake, and a flash goes in a sailboat, is it dangerous for me?

and the second one,
If I stand next to a building holding the lightning rod, and a flash goes into the building, am I in danger?

I would ask my physics teacher, but during holidays, thats not so easy. ^^

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Stats : 4 Replies

Rubik's Cube

Mon, 26 Oct 2009 22:36:15 GMT

Basics : Rubik's Cube

Not sure if this is the right board to post this, but I was just wondering if anyone knew links to a good site explaining the quickest algorithms to solve a Rubik's Cube. It takes me 5 minutes, and the world record is about 9 seconds, so I know I'm missing something!

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Stats : 12 Replies

Can 1 plus 1 prove to be something else?

Sun, 25 Oct 2009 13:24:02 GMT

Basics : Can 1 plus 1 prove to be something else?

I remembered many years ago, in my Secondary Four days, a student came forward and presented a chalkboard full to equations and concluded that 1 + 1 = something else. I cannot remember, but the whole class surely could not find any error in the logic based on maths theories we are familiar with.

Is there anyone out there who could help to refresh these equations?

I am still puzzled, but could not review them, as chalk marks on a chalk board are cleared, as soon as we rub them off with a duster.

Hope to rekindle the old fun in maths for myself.

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Stats : 34 Replies

Probability Problem

Sun, 11 Oct 2009 11:56:06 GMT

Basics : Probability Problem

Despite taking further mathematics, I appear to have completely forgotten statistics. In doing some work (for myself) I have come upon a problem that I haven't managed to solve, despite much though.

So here it is. We have an x by x grid/table of cells (like a chess board). Each cell initially contains a 0. I sequentially apply an operation f a number of times n. The operation f randomly selects a cell and switches its value; if it's a

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Stats : 6 Replies

Engineering Mathematics

Mon, 05 Oct 2009 12:05:25 GMT

Basics : Engineering Mathematics

Enginering mathematics touches all topics of mathematics espicially if you are doing a course in computer engineering.
for maths lovers, it is great.

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Stats : 7 Replies

Statistics Help

Mon, 28 Sep 2009 18:00:29 GMT

Basics : Statistics Help

So I'm faced with a much bigger stat problem, all I need to know to continue on my proof is:
- what are the assumptions needed to get the standard error of a proportion
- how do you approximate the standard error of a proportion given p (proportion) and n (number of samples).

I found a site that says:
SEp = sqrt[ p * ( 1 - p ) / n ]

but I'm not quite sure how they got it.

Anyone willing to explain to me how to estimate it?

Thanks in advance.

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Stats : 2 Replies

Capacity of Air conditioner

Mon, 28 Sep 2009 02:03:51 GMT

Basics : Capacity of Air conditioner

Hello
What should be the capacity of an air conditioner to cool a Room of 150 X 50 X20 feet room. It houses about 30 people on an average. The room has 10 computers.

Thanks in advance

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Stats : 2 Replies

Visual atomic physics

Sat, 26 Sep 2009 05:43:01 GMT

Basics : Visual atomic physics

There have been a couple of really awesome developments in atomic physics the last couple of weeks that have gone unmentioned here. Most of these developments are more cool than groundbreaking, and mostly about making long-held physics theories

visual

.

The first is an image taken of a single pentacene molecule - which is a molecule made up of five linked benzene rings. It is the first image taken of a single molecule (we have imaged

atoms

before, both by themselves and in crystalline structures, but never

molecules

because they are so fragile). You can clearly see the benzene ring structures, and the carbon-carbon bonds in the benzene rings, and if you squint you can even make out the hydrogen atoms on the periphery (they're the smudges that extend away from the outside vertices of the hexagons).

(source: http://news.bbc.co.uk/2/hi/science/nature/8225491.stm)

The second is an image of a single atom, but such a clear image that you can actually make out the individual electron orbitals. In this image, you can see the 1

and 2

orbitals as blue clouds. This is a neat way to show that quantum mechanics is probably right.

(source: http://insidescience.org/research/first_detailed_photos_of_atoms)

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Stats : 5 Replies

Warning about copy-paste

Wed, 23 Sep 2009 19:31:58 GMT

Basics : Warning about copy-paste

I've noticed quite a few 'copy-paste' postings appearing in the science forums. This won't do at all. Simply copying a chunk of text from another site and posting it here as your own is not within the TOS. Use quote tags, acknowledge the site the material comes from, and add something of your own. Otherwise I will simply delete any such posting and issue a warning to repeat offenders.

If you don't know how to quote third-party material properly:

enclose

QUOTE

in square brackets at the start of the copied passage
enclose

/QUOTE

in square brackets at the end of the copied passage

Be sure to add your source as an http reference at the end of the posting or passage.

Here is how it should look (thanks to James007 for the visual aid).

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Stats : 1 Post

Math Induction?

Thu, 17 Sep 2009 01:59:09 GMT

Basics : Math Induction?

I am tutoring a student on PreCalc and he is learning about a process called Math Induction. Can someone offer any background on how this works? Practice problems would be helpful!

I have looked at Wikipedia, but the explanation is kind of convoluted.

Thanks,
G

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Stats : 7 Replies

Live Animated 3D Webpage

Sat, 12 Sep 2009 18:57:17 GMT

Basics : Live Animated 3D Webpage

I just added a new interactive web page.
Can you work in 3D and avoid making objects that collide with each other?

Go over and have a look at:
http://www.irunmywebsite.com/raphael/xyz_3d_Platonic_live.html

If your there for more than 20 seconds then come back and tell me what you did and how you made out!

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Stats : 3 Replies

How do you define mathematics?

Sun, 06 Sep 2009 12:22:44 GMT

Basics : How do you define mathematics?

How do you define mathematics? I took a watered-down physics class where you needed limited math skills. The teacher gave us all a sheet full of equations that he allowed us to use on the tests. I thought that that was ridiculous, but he said that he wasn't testing us on our memorization skills; he was testing us on our knowledge with using them. My friend and I never used those; we both knew calculus and we did the math on all of the physics problems and tests. With math, my friend and I managed to derive these formulas that he gave us. Because of this, I used to consider math to be a science. However, after reading this http://www.frihost.com/forums/vt-76771.html post, I realized that mathematics cannot be considered science. It does not follow the scientific method, and everything is proved in math. In science, nothing is proven. ...

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Stats : 45 Replies

CO2 can't be liquid in open air?

Sun, 06 Sep 2009 06:39:58 GMT

Basics : CO2 can't be liquid in open air?

I read somewhere that CO2 can't be liquid in open air. Can some one explain why?

...
Let's say you have some compressed CO2 you let it out of the gas tank wich causes it to freeze (CO2 snow) and then let it in the open air. Or you just take a block of dry ice. It will go directly to it's gas form and it will skip the liquid part (Sublimation).

But why o why doesn't it get liquid first?

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Stats : 9 Replies

The photon and E=mc^2

Sat, 05 Sep 2009 22:21:59 GMT

Basics : The photon and E=mc^2

I'm having a little problem with understanding the 'massless' photon...
If we use the equation E=mc^2, on a photon, using zero for the mass, we get E=0*c^2, reducing to E=0.
So, if a photon has no mass, then it must also have no energy.
But, suppose we start with the other variable known (I'll assume the value of it is '2', since I don't know the real value, and it doesn't really effect my point.) Then we have 2=mc^2, after solving that, we'll end up with the result of the photon having a tiny, but definite mass. The problem with that, though, is that if it does have any mass at all, the mass of it should effectively be infinitely large (according to relativity), since it is traveling at the speed of light.

Anybody have any insights to help me out of this conundrum?

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Stats : 12 Replies

Pi: a fractal?

Sat, 05 Sep 2009 22:20:28 GMT

Basics : Pi: a fractal?

So, I've been thinking about pi lately, and wondering if there could be a pattern to the seemingly random sequence of digits within it. Then I thought of something else that goes on and on without repeating:

So, I thought, could a fractal number go on and on without repeating?

I made a quick program in C++ to find out for sure, and it looks like one can.

The algorithm goes like this:

Code:

a = 0
b = 0
c =0
d =0
e =0

>>repeat from here<<
1:
a ++
e ++
output & test for repeat of first "00000"
2:
a ++
c ++
e ++
output & test for repeat of first "00000"
3:
a ++
b ++
c ++
d ++
e ++
output & test for repeat of first "00000"
>>repeat<<

This creates a sequence of numbers that progresses like this:
00000
10001
20102
31213...

When it is all run into one long string, it looks random, but actually is not. The first sequence does show up occasionally, as it also would in a random number, but the numbers following it are never the same as the numbers following the first group of five.

What I was wondering is, could pi also have a pattern like this within it, and if it did, would it be possible to find it?

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Stats : 17 Replies

Internal resistence change

Sat, 05 Sep 2009 22:10:36 GMT

Basics : Internal resistence change

In potentiometer experiment in our lab, internal resistence of a cell (leclanche cell) incresses with external resistance! Which is against theory, can give an explanation?

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Stats : 6 Replies

how many rectangles are in the chess board?

Wed, 02 Sep 2009 18:29:58 GMT

Basics : how many rectangles are in the chess board?

guissmo wrote:

Now let's screw everyone and ask how many rectangles are in the chess board. )

Hi guissmo

I think this problem deserves a thread of its own!

Any rectangle on a chess board will be w by h units, where 1≤w≤8 and 1≤h≤8.

Obviously there are 8 x 8 = 64 different possible shapes, but they can be positioned in many different ways. To describe the position of a rectangle, let's use an x-y coordinate system on the chess board, taking ats bottom left hand corner as the origin, so that (x,y) represents the point x units to the right and y units up, where 0≤x≤8 and 0≤y≤8.

If we place a w by h rectangle so that its bottom left hand corner is at (x,y), then it's top right corner will be at (x+w, y+h), so we must have x+w≤8 and y+h≤8. That is, x≤8-w and y≤8-h. So we have 0≤x≤8-w and 0≤y≤8-h. This gives 9-w possibilities for x and 9-h possibilities for y, or (9-w)x(9-h) ways of placing a w by h rectangle altogether.

Taking all different possible sizes of rectangle w by h, this gives:
Sum (w from 1 to 8 ) Sum (h from 1 to 8 ) of (9-w)x(9-h)
= Sum (w from 1 to 8 ) of (9-w) x Sum (h from 1 to 8 ) of (9-h)
= Sum (w from 1 to 8 ) of (w) x Sum (h from 1 to 8 ) of (h)
= (½ x 8 x (8 -1))^2
= 28^2
= 784

In more readable mathematical notation, this is:

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