Interesting Definition and 790 Threads

Thought this Tim Gowers post was quite interesting.

2^2-1 = 2^2-1 = 1^2+2 2^3-1 = 3^2-2 = 2^2+3 2^5-1 = 6^2-5 = 5^2+6 2^13-1 = 91^2-90 = 90^2+91 I realize that x^2-(x-1)==(x-1)^2+(x) 2,3,5 and 13 are all the powers of mersenne primes, and are Fibonacci numbers as well. It'd be interesting to see what's the next power of 2 that satisfies...

In another thread (on Oppenheimer-Snyder collapse), I posted a link to some lecture notes on gravitational collapse. Checking on the author, I find he is extremely prolific on many fundamental areas of GR (from the computational standpoint). Of particular interest...

Homework Statement Let T be a square nxn matrix and let each entry tij=n(i-1)+j. Calculate the eigenvalues of T of T when T is a 3x3 matrix and a 4x4 matrix. Homework Equations The Attempt at a Solution For the homework I'm supposed to calculate the 3x3 case and the 4x4 case. Then it says...

So recently I have gotten in a heated argument with my friend about heating his apartment (no pun intended). Here is the argument: My EE friend has a theoretical heater which runs on 1000 watts of power. In his apartment he also has another electronic device (ie. a computer, a television...

The recent report from the South Pole Telescope seemed to several of us to be exceptionally interesting making one think we might have a thread that just lists recent papers, as they come out, which seem as if they might be important to cosmology. Here are a few. http://arxiv.org/abs/1210.7231 A...

An interesting question has been posted in... Infinite Series Conditional Converging ... about the following two variables function... $\displaystyle \sigma(x,y)= \sum_{k=1}^{\infty} \frac{1}{(k+x)\ (k+y)}$ (1) ... and in particular it has been requested if the domain of $\sigma(*,*)$ must...

Homework Statement http://img210.imageshack.us/img210/2082/93284166.png http://img210.imageshack.us/img210/2082/93284166.png Find the correct reactances for the impedances so that the current in the neutral/grounding wire would be 0 A. (IN=0) Phase voltages are 231 V, and the voltage between...

Hope you enjoy the following, http://www.youtube.com/watch?v=_Ssc1GsqHds&feature=player_embedded From, http://planetsave.com/2012/10/20/galaxies-trend-towards-more-ordered-disk-like-forms-over-time-upending-old-assumptions/

Homework Statement What is the angle of elevation of a projectile that travels THREE time horizontally its MAXIMUM height, on earth g = 9.800m/s2Homework Equations Equation 1 - H = ((vsinθ)2)/2g Equation 2 - R = 2v2((sinθcosθ)2/gThe Attempt at a Solution I tried making 3x(equation...

Homework Statement A bullet of mass m = 17.6 g traveling horizontally at speed vo = 565 m/s strikes a block of mass M = 678 g sitting on a frictionless, horizontal table. This time, however, it comes out the other side of the block at speed v = 524 m/s. Calculate J, the magnitude of the...

I have to present an investigation on a topic that is related to healing and cooling. In class we're studying kinetic theory, ideal gas laws, heat, temperature, specific capacity, change of state, boiling and evaporation, energy conservation and degradation, and the transfer of heat. Are...

This is very interesting, is it the first proposed method (that is within reasonable energy for particle accelerators) to test space at the plank level? http://arxiv.org/abs/1207.7297 Testing Planck-Scale Gravity with Accelerators Vahagn Gharibyan Abstract: Quantum or torsion gravity...

The interest of this article was first pointed out by Tom Stoer in biblio thread comment. The idea is to take seriously the quantum nature of geometry and its interaction with fermions at the quantum level. The idea is even that geometry might be as we experience it BECAUSE her little triads...

An interesting pair of problems has been proposed in… http://mathhelpforum.com/pre-calculus/203756-geometric-sequences.html Now we try to solve #74 that looks like a ‘yellow roman’… Consider the sequence… 4 , 20.4 , 104.04 , 531.6444 , … What is the error in using $a_{277}= 4 \cdot...

So, I think I have done a thread here with some questions related to academic guidance before... when I was a tad younger. (https://www.physicsforums.com/showthread.php?t=561141) Well, I'm a Brazilian student, I'm in my senior year in high school. It is very likely that I will study Physics...

Homework Statement So each box in the picture has resistance R. Find the resistance between A and B. Homework Equations R=R1+R2 1/R=1/R1+1/R2 The Attempt at a Solution I got the answer to be 3,5R. But as I am not sure if I approached the problem correctly, I would like to...

The Aperiodical | #MTT2K: Teachers critique Khan Academy The title is misleading to some extent, it is the second video that I think is most interesting. CB

Hi everyone, first off i'd like to thank you all for maintaining this awesome forum, seems really cool :D I wasn't sure whether this should be in the homework forums or not, but since I'm not asking for any solution of some sorts, i decided to post here. I'm a senior high school student...

Hi all, I need to solve this problem for my environmental chemistry class. It is supposed to be a "review" problem of concepts from analytical and gen. chem. but I certainly do not know how to do it. Homework Statement If you work at the wastewater treatment plant, you are exposed to...

So I was brainstorming:bugeye: trying to find what I did wrong in this chemistry problem: https://www.physicsforums.com/showthread.php?t=627731 (simple algebra no chemistry knowledge required) And I noticed something peculiar about the process of solving inequalities, let me sum up in a phrase...

Does anyone know of any books that will get younger people (teens/pre-teens) interested in physics (or science in general)? Maybe something like Feynman's 'Six Easy Pieces'?

"Quantum measurement predictions are consistent with relativity for macroscopic observations, but there is no consensus on how to explain this consistency in fundamental terms. The prevailing assumption is that the relativistic structure of spacetime should provide the framework for any...

I just came up with a problem I hope you will find interesting, but I can't seem it solve it myself. I thought of induction as some guide, but am not sure how to proceed. There are N terms in some finite arithmetic progression. Two of those terms are equal to 3. Prove that all terms in this...

Hello colleagues! I’d like to ask your opinion on the following information. I found an article where is talking about wonderful polymer that has very interesting properties to pick up parameters when applied on some surface including human body and to register information and to transfer...

Hello, I was browsing a set of number theory problems, and I came across this one: "Prove that the equation a2+b2=c2+3 has infinitely many solutions in integers." Now, I found out that c must be odd and a and b must be even. So, for some integer n, c=2n+1, so c2+3=4n2+4n+4=4[n2+n+1]...

So I need to come up with an experiment to do a 3500-4000 word essay. The types of topics I'm interested in are satellites, planetary orbits, etc. I guess mainly classical physics. Some topic ideas I came up with are: 1. At what height do you have to drop a marble so that it goes through a...

Homework Statement A block of mass M rests on a ramp inclined at an angle z. there is a coefficient of friction s between the block and the ramp. The ramp itself rests on a horizontal, frictionless surface and is held away from the wall by a spring with spring constant k. What is the...

I have a hand held night vision scope (Russian made I suspect.) Came with a small Solid State IR "lamp." The IR source is separate and battery powered. It has a built in hand operated charger that you squeeze several times and it will hold a "charge" on the sensor for a while and then...

Okay, so I've recently been reading through C. Pozrikdis' Introduction to Theoretical and Computational Fluid Dynamics, and came across an interesting exercise: "Discuss whether it is possible to label all point particles within a finite three-dimensional parcel using a single scalar variable...

Hello all, I am a Pre-Junior at Drexel University Mechanical Engineering Major. I am entering the BSMS program this fall. I need to choose a specialization for my Master's Degree. I have three choices - 1. Mechanics 2. Thermal Fluid Sciences 3. Control Systems. As my title states...

Has anyone ever noticed that, even in classical physics, energy is shown as a scalar multiple of mass? For example, consider the joule; 1 J = 1 kg*(m/s)^2 If you consider the units of motion (m/s) to be a vector quantity, then squaring such a vector would be interpreted as a dot product...

Homework Statement NxNx[0,1) is homeomorphic to [0, 1). Find an explicit homeomorphism. (Note that N=naturals) Homework Equations A function f is a homeomorphism if: (1) f is bijective (2) f is continuous (3) f inverse is continuous The Attempt at a Solution Finding a map from...

\text{We have: }\:\dfrac{1}{89} \;=\;0.01123595\,\,.\,.\,. \text{The decimal is formed like this:} . . 0.0{\bf1} . . 0.00{\bf1} . . 0.000{\bf2} . . 0.0000{\bf3} . . 0.00000{\bf5} . . 0.000000{\bf8} . . 0.000000{\bf{13}} . . 0.0000000{\bf{21}} . . 0.00000000{\bf{34}} . . . . . . \vdots...

Without the classic method of "completing the square" and factorising?

Here's a leaflet which was distributed over Germany and Poland, apparently during the year 1944 (as it refers to the drop tanks which would have been regular equipment aboard the P-51 Mustang long-range escort fighters then being fielded by the 8th Air Force), by the National Socialist...

Hi guys, I've been playing around with structure generated patterns and have come across one which has caught my attention. I am only just starting to learn about number theory and so I am sure someone might be able to provide an explanation for this. Let me describe what I did then show you the...

If you are in need for some humiliation, try some of the IQ test questions here: http://www.triplenine.org/. Hit "Links" at the top of the home page, then link to "Links to high-IQ related websites", then link to "Uncommonly difficult IQ tests". Or just prowl around the website -- lots of...

Interesting discussion on the "crisis in higher education" Hi everyone. I have found the following interesting post regarding the "crisis" in higher education (a topic brought up in numerous posts here on Physics Forums) from the blog of Aaron Clauset, a physicist turned computer scientist, and...

Hello PF, I am a Sophomore in high school in the US and have already led what I would consider to be a pretty awesome life, but I have an interesting dilemma. All my life I have loved to ski, I ski competitively, and I believe that if I continue to pursue skiing I could possibly become a...

I have a group of young people (aged between 15 and 18) interested in doing a project that combines astrophysics and biology; could anybody recommend any good projects or research tasks for them?? For difficulty wise they have already completed an advanced gold crest project in astrophysics...

I'm a physics teacher and one of my AP students posed the following question: "if there was a steel bar 2 light years long and you moved it forward a couple inches, would the other end move forward a couple inches immediately or would there be a delay?". We'd been discussing electric fields, so...

\displaystyle\frac{1}{998,001} \;=\;0.\overline{000\,001\,002\,003\,004\,005\, \cdots\,996\,997\,999}\, \cdots The decimal representation contains all the 3-digit numbers except 998 . . and the 2997-digit cycle repeats forever. This is just one of a family of such fractions. Can you determine...

I am writing an undergraduate "thesis" on group representations (no original work, basically a glorified research paper). I was wondering if anyone could suggest interesting aspects that might be worth writing about in my paper. I have only just begun to explore the topic, and I see that it...

I am taking a course on Java and i am looking for some interesting general programming problems i could solve with java. I've gone through two java books, but most of the exercises at the ends of the chapters are very straightforward, and I am looking for something more challenging. My...

Please derive the right-hand side from the left. If anyone could shed some light on this I would be grateful. \frac{d^{2}}{dx^{2}}\int_x^{∞}f(x,z)g(z)dz = \int_x^{∞}f_{xx}(x,z)g(z)dz - g(x)(f_{z}(x,x) + 2f_{x}(x,x)) - f(x,x)g'(x) Please, if you can, provide a detailed explanation of...

Homework Statement Hello, I now have a real practical mathematical problem to ask I have 14 files with different sizes to be burnt on DVD discs. Each DVD disc is 4.7GB. How to arrange the files so as to minimize the use of discs? The file sizes of the 14 files are 1) 2.25GB...

First, I apologize for any awkward language--I'm still relatively new to mathematics. This problem seems to be related to number theory as well if it pans out, but I thought it would be better suited here. Given a point (x,y), can you always construct a circle such that the center of the circle...

Do you flip a coin or what? Looking at course descriptions, I found everything ranging from EE (especially the bio applications) to geophysics to be interesting. I understand that between physics and engineering, the core courses will be very similar for the first year but still, I was wondering...

I'm to do a presentation in two weeks about physics, and I'm wondering what would be interesting to my classmates? (no, I can't ask them, I won't be at school during that period of time) I was thinking to talk about physics in video games, but it's too technical in my opinion, therefore it...