Interesting Definition and 754 Threads

I've come up with a scenario which seems to be something of a paradox to me: Imagine, if you will, two similar rotating objects orbiting each other at a fixed distance, sharing the same rotational plane. These two objects now experience acceleration to some fixed speed along their shared axis...

Long back (not so much long back), when I was first introduced to complex numbers, my mind was flooded with strange and interesting curiosities (as they appeared to me!), rather ideas. Of course this realm of mathematics is, as the mathematicians are fond of saying, is remarkably beautiful. As I...

A friend asked me for an interesting way to destroy a boxful of flashcards for a video scholarship. Being almost the 4th of July, I mentioned making some kind of fireworks out of them, but I want to give him something a little more... safe and legal. I tried looking on Google for chemical...

I found an interesting limit: any ideas? :)

Happened to go to a group of fundamental pentecostal families for a music night, where we spent the evening singing pop songs. We were singing a few devotional songs too, as expected. I randomly sang a virgin Mary devotional song, and everyone started looking at me as if I spoke some profanity...

Hello all, I am a fourth year at uni, getting my degree in applied mathematics with a minor in computing. I've taken classes in physics (electromagnetism and circuits) and lots of programming... and recently landed a co op position as an electrical engineer in a large (14,000+ people) medical...

http://www.nbc.com/americas-got-talent/video/week-1-night-2/1232101/ watch starting around 5:35...' explanation??

Recently, I have come across some interesting studies of sound called 'Cymatics'. I was curious in how the modern scientific community views this intriguing field of research... Can anyone help to enlighten me on the subject?

Suppose I put 1 kg of -10-degree ice in a 1 m^3 vacuum chamber. How much heat do I have to add to turn all of the ice into vapor at 100 degrees Celsius? This seems like a ridiculously simple problem, but I realized I've no idea how to solve it. First of all, ice sublimates in a vacuum...

Homework Statement Suppose f is continuous and F(x)=\int_a^x f(t)dt bounded on [a,b). Given g>0, g'\geq 0 and g' locally integrable on [a,b) and lim_{ x\rightarrow b^-} g(x) = infinity. prove for p>1 \displaystyle{lim_{ x\rightarrow b^-} \frac{1}{[g(x)]^p} \int^x_a f(t)g(t)dt = 0}...

I hate a piece-wise function f(x)= [ 1 if 0 </eq x </1 [ 0 if 1 < x < 2 [ -2x+4 if x >/eq 2 If I let F(x)= integral (from 0->x) f(t) dt, how can i find a formula for F(x) without using integrals? I think it may have something to do with the 2nd definition of the...

Suppose that a set S has the property that all of its members are integers and that the average of any 3 of its members is not an integer. What is the maximum number of elements that S may have?

While messing around with the Schrödinger equation on paper, I found an interesting, elegant way of expressing it. Let P be the probability density |\Psi |^2, and let \vec Q be a real-valued vector field. \vec F is a vector field describing the forces acting on the system when in a given...

Hi, what I did to try to find prime numbers was this (in a computer program) Starting from 2, I set off a sine wave that has an amplitude=0 for every even number and an amplitude=1 for every odd number. What we are looking for, then, are the portions of the sine wave where the derivative...

I am doing a report and presentation on Erwin Schrödinger in my physics class and I want it to be exciting and interesting. Does anyone have and interesting facts about this great scientist? Not just FACTS, but INTERESTING facts! I have heard that he was quite the ladies man... Thanks! ~Matt

I am still far too much of a newbie to be able to intelligently speak on any of the items listed in this website, but it all seems very interesting. Will anyone comment on the veracity of this article, and if it's really as "cutting edge" as they make it sound? I find item #3 particularly...

I'm in my 4th year of a physics program, and I've got some serious freedom choosing courses now. Has anyone taken graph theory? I've got a basic idea what it is, but no clue how difficult it might be. Any other good math courses to take as an option that won't bee too difficult? For...

\lim_{n\to infinity}{{(\sqrt{n^{2}+n+1}})-[{(\sqrt{n^{2}+n+1}})]} wer [.] is GIF how will u solve this one

I'm afraid the template for homework help doesn't quite apply here since my problem is the lack of a problem in itself. I'm an International Baccalaureate student, and I've decided to do a research topic (about 4000 words) on physics. I need help with this. I'm looking for suggestions for...

hey everyone, My class was thinking about buying a present for our physics professors. We are currently studying for A-Levels. as it is his last year of teaching. So I just wish to tell you the situtation -our prof is graduated in physics and maths -our prof told us that once he got...

I am having a tank at the bottom of which a pump suction line is connected.. there is another parralel line to that bottom line which is coming from another tank and open to atmospheric pressure. Please note that this second pipe is connected to the bottom pipe; not to the first tank...

Hello, I have a question Lets say you have a container of water that weighs 10 pounds including the water/container material and u have a 5 pound object that can float quite easily in that water and u attach a piece of string to that object to the bottom of the container of water to the...

A 2 gram Magnesium (Mg) ribbon is burnt in air . The burnt ribbon is collected and weighed. Would it be greater than 2 grams or lesser?

I found this experiment on YouTube, and its about interference pattern variation in a vertically spinning interferometer.. http://www.youtube.com/watch?v=7T0d7o8X2-E&feature=related

"Did You Know..." Our department has bulletin boards for each faculty member; I'm looking for ideas on what to put on mine. The idea is for each member to advertise themselves to the (undergraduate) student body- not just majors, but any student that wanders by. My wife came up with a 'Did...

Some interesting brainteasersStarterI used Some interesting brainteasers Starter I used factorials for this one, but it will be interesting to see how you attempt your answer. Head Scratcher These questions are designed so that anybody above the age of about 13 can answer...

Some interesting brainteasers Starter I used factorials for this one, but it will be interesting to see how you attempt your answer. Head Scratcher These questions are designed so that anybody above the age of about 13 can answer them without much mathematical experience. If...

Hello, I have a few questions that I have made myself, but I don't know how to answer them. 1) Say that there is an isosceles triangle ABC. Two of the equal angles are 1/∞. What is the other angle? 2) Is a sphere really a sphere if you can draw a tangent to it? 3) Assume that there...

I have some very vexing questions regarding light. We seem to know so little about it. 1. What happens to light when it is not traveling ? 2. Does it accelerate in reaching C ? If not does it "jump" to C ? 3. Can it be destroyed ? If not it seems to me that the amount of light in the...

suppose i want to find the following integral: 7 \int[SIZE="5"]x dx 3 now suppose for some demented reason i decided not to do it straightforward and get (49-9)/2=20 instead i use the substitution x=u2+4u+5 giving u1 \int[SIZE="5"](u2+4u+5)(2u+4)du u0 u1 \int[SIZE="5"]2u3+12u2+26u+20 du u0...

I'd purchased a http://en.wikipedia.org/wiki/Mosquito_bat" recently. These things are very handy for swatting mosquitoes in the rainy season. A little while ago, I noticed something curious while swatting: after I hit the creature, it falls on the floor and begins to spin rapidly. Many a time I...

There is a popular myth that after drinking a bottle of water, the last bit is mostly backwash. Well I decided to try and test it, but got stumped. Lets call y the amount of backwash in the bottle Lets call x the number of sips taken The volume of the bottle will be 1000mL Assume each...

Hello, Chemistry grad student here about to start a physics-y project...so trying to learn about condensed matter physics. I get how screening works when you add a single charge to a gas of electrons, but what happens in a metal when you have a whole lattice, ie, a background charge density...

Draw a cylinder, with diameter D and length/height infinity, mark the top point Y and the bottom point Z Now Say a person falls into this cylinder/hole. (there are equal sources of light emitting into each end of the tube) From the falling person's perspective the point Z looks like an...

its from mensas website so it can't be too bad. i was just curious how you guys would do. i made sure to keep my time down to 30 minutes (although i did it in 32 minutes). i got a 20/30 on it which apparently is good enough to pass the real test... just thought id share it with you guys, since...

Hey there, I have to make a presentation about a technical topic in my technical spanish class. Since I have to hold the presentation in spanish and the listeners aren't experts either, I would like to choose an interesting topic which does not include too much jargon. I was considering...

So I've been working on this for a while now, but I'm a little stuck. I think I see how to solve the problem below, just need a couple tips to get me over the hurdle. Homework Statement There are two infinite wires in the same plane as a rectangular loop. Geometries are displayed in the...

Well I have been teaching my self mathematics for about 4 months now. Started with pre-algebra now I'm on "modern algebra". Thing is I haven't taken geometry in high-school(and will not be able to). So I'm looking for a quick book that is interesting enough to keep me well, interested. I know...

I and a few other freshman are in a seminar that's intended to help us in E & M and requires us to bring questions and problems to the seminar to work on. We've been doing some textbook problems, but it would be better if we could find something more challenging or conceptually interesting so...

Homework Statement I recently was given an interesting problem I thought I'd share with the community here. It's a fun exercise in mathematics. Given the equation: Po/P = [1+((k-1)/2)*Ma^2]^(k/(k-1)) From this stagnation ratio, derive the Bernoulli Equation: Po = P + 1/2 * rho * V^2...

Homework Statement http://www.kent.k12.wa.us/pcpow/questions/calc/0401trickortreat/index.html This is an old problem, and I have been able to solve one and two, I believe the answers are 1. pi cm/second 2. 50(pi) cm^3/second 3. This is the one I am not sure of. How can I solve...

Homework Statement A person throws a ball off a roof that is 8 meters high with an angle of 45 degrees from the positive x axis. The ball is supposed to land in the center of a square that is centered 9 meters away from the base of the roof. With which initial velocity must the person throw...

Ok so here is a brainteaser, you should get it in your second attempt at the max., else consider yourself poor at math :biggrin: An ant is in one corner of a cube shaped room. (say one of the bottom corners on the floor). The ant decides to go to the opposite corner on the roof, which would...

Hi everybody, On a probability theory lecture I met an interesting problem: Let f : [0;1] -> R a bounded, 3 times continously differentiable function. Calculate the following limit n * \int_0^1 \int_0^1 ... \int_0^1 f(\frac{x_1+...+x_n}n)-f(0.5) dx_1...dx_n while n -> infinity Any ideas?

Hallow I want to know why if I throw 2 balls and one ball is bigger and whit more mass Why the two balls arrive to the ground in the same time This is the experiment of glilio glili Also I search after more experiment in mechanics (physics) like this Or like this experiment - if I throw a...

Homework Statement Let x=(1,0,0) y=(2,1,0) and z=(2,2,1) be column vectors in R3. Consider the set V={tx+sy+uz 0\leqt,s,u\leq1}. What does this look like specifically? Homework Equations n/a The Attempt at a Solution No work here, just a thinking problem, but I thought that...

I would have thought this standard crackpottery, but evidently it won "Best New Paper" from the University of Liege in Belgium! What do you all think? http://www.theresonanceproject.org/pdf/schwarzschild_proton_a4.pdf I can't find anything about the "quantum vacuum density" he talks...

http://www.sciencedaily.com/releases/2009/08/090811143716.htm Water is familiar to everyone—it shapes our bodies and our planet. But despite this abundance, the molecular structure of water has remained a mystery, with the substance exhibiting many strange properties that are still poorly...

Homework Statement At the top of a pole vault, an athlete actually can do work pushing on the pole before releasing it. Suppose the pushing force that the pole exerts back on the athlete is given by F(x) = (160N/M )x - (180n/m^2 )x^2 acting over a distance of 0.24m. How much work is done...

What are in your opinion the most interesting areas or topics in foundational physics? (that have or could have profound philosophical implications) I want to see what's out there.