Interesting Definition and 790 Threads

A standard 8x8 chess board has but a lone rook in the bottom left corner. A rook a piece than can move any number of spaces either horizontally or vertically. If the rook can only move up and to the right, how many possible paths does it have to the top right corner? I think it's a pretty...

Homework Statement Assume the wooden ruler is balanced and that it has uniform density. If the wood is replaced by metal, increasing the mass and density of the ruler without changing its dimensions (and remaining uniform), the ruler will... (Assume the length of the ruler is 1 meter.) Looks...

We solved a simple looking heat diffusion problem because it describes an apparatus used in an NIH sponsored research project. It resembles problems discussed in textbooks and in many papers on the web. A textbook method solves all those problems but a straight forward application of that...

Hey all. I am giving Panhellenic exams this year, and part of my preparation comes from solving previous' years questions. This problem was a complex number based one, in the 2013 Panhellenic exams. It goes as follows: Consider 3 complex numbers, α0,α1 and α2 which belong in the line given by...

Hi, I find an interesting related to electric field when doing experiment. I put a chip which has the following circuit inside Scanning Electron Microscopy(SEM), an electron beam is irradiating on R1. The AC source is isolated from Earth by using a capacitor C1 and resistor R3 in the...

I thought this was an interesting article on dark matter, what might this kind of DM be made from? I also wondered could DM help explain in some way where all the anti matter ended up? http://www.space.com/27794-dark-matter-destroying-neutron-stars.html

Homework Statement A particle moving from a point A to a point B , 1 meter away, travels in a straight line in such a way so that its acceleration is proportional to the distance left to point B . If the particle arrives at point B in 1 second, how long did it take for the particle to...

Homework Statement I recently searched around SE, and found: http://math.stackexchange.com/questions/1142546/how-to-solve-this-derivative-of-f-proofHomework Equations Below The Attempt at a Solution The answer is interesting. "A function given that $$f(x)=f''(x)+f'(x)g(x)$$ could be an...

I will be doing a presentation in the science symposium at my community college. The common theme is always topics from biology or chemistry but never from physics or mathematics.. I am a Math major and love pure mathematics, I am interested in presenting the great theorems of mathematics...

Is there any way of evaluating the following integral: \int sin{(\frac{2x+3}{x^2+3x-2})} dx I have thought hard but cannot find an answer. Obviously, the denominator is the differential of the numerator. But a function is being taken of this fraction...

This YouTube has some interesting archery demonstrations:

Homework Statement Not actually for homework, but i didn't know where to post this. Problem: Show that any integer to the fourth power can be expressed as either 5k or 5k+1 where k is an integer. Homework Equations None. The Attempt at a Solution My starting point is to consider that all...

Hey! I have to do a work about one of the many applications of mathematics. I have to study the math behind a certain subject and use MATLAB to solve some kind of problem associated with the topic. I am on the final year of graduation and I thought of doing about optics, fractals, relativity or...

Digital root (adding a number's digits together repeatedly until a single digit answer is obtained) doesn't seem like a very interesting operation, but it has some weird properties. One of the first someone might notice is that dr(n) = dr(n+9) This is fairly easy to demonstrate. But after...

So a year ago I tried an accelerated paced computer science course when I had no experience programming and I ended up hating it and dropping due to never understanding what was going on. Now I finally decided to take a intro to programming class that is pretty cool, but still no where near as...

So, I would like to prove that \gamma^{\mu_{1}...\mu_{r}}=(-)^{r(r-1)/2}\gamma^{\mu_{r}...\mu_{1}} where the matrix gamma is a totally antisymmetric matrix defined as \gamma^{\mu_{1}...\mu_{r}}=\gamma^{[\mu_{1}}\gamma^{\mu_{2}}...\gamma^{\mu_{r}]} What I have done is to prove that...

Homework Statement Find the x-component of the ##F_b## (parallell with ##\vec{s}## and the ground) and find the resultant total Force. Then calculate the total work done by both over a distance of 15 m. Homework Equations F_{x} = |F| \cdot \cos v F_{y} = |F| \cdot \sin v W = \vec{F}...

Good day all, someone gave me this problem to try to figure out (for fun) and I'm having a bit of a hard time: A closed cylinder of radius R and length L is filled with liquid. The volume of the liquid is equal to 1/3 the total volume of the cylinder. If the cylinder is layed flat (horizontal...

I am wondering what the first steps are to finding an interesting calculation, and doing it. My adviser seems concerned only with me writing my thesis to hurry up and get me out of the program, rather than helping me develop my CV and involving me in other calculations he may be doing. It seems...

Homework Statement A piston‐cylinder initially contains 0.5 m3 of an ideal gas at 150 kPa and 20 degrees. The gas is suddenly subjected to a constant external pressure of 400 kPa and it is compressed in a manner that the final temperature is also 20oC. Assume the surroundings are also at 20...

I am learning about statistical design of experiments, and in the process of mathematically rigorizing the concepts behind fractional factorial designs of resolution III, I derived an interesting equation: $$k = \sum_{i=1}^{3}{\lceil{\log_2{k}}\rceil \choose i},$$ for which the solutions $k$...

Helllo, I have found another interesting integral from the old Putnam's. Please ONLY use the "differentiation under the integral sign" rule for this one, after we have done that we can explore other possibilities. I really want to try "differentiation under the integral sign" for this...

Hi, $$\int_0^1 \frac{\ln(x +1)}{x^2 + 1} dx$$ It is supposed to be done by "differentiation under the integral sign" rule. So we being by making a general form, $$\int_0^1 \frac{\ln(x +1)}{x^a + 1} dx = I(a)$$But before I start anything, I am very clueless because I am fairly new to the...

Seems like good career guidance no matter what career you get into: https://www.linkedin.com/today/post/article/20140728185743-658789-8-slow-difficult-steps-to-become-a-millionaire

Homework Statement Problem 63 from Gelfand's book Algebra asks "are the father of the son of NN and the son of the father of NN the same person?" Homework Equations This problem is in a section about the square of a sum formula. (a+b)2 = a2+2ab+b2 The Attempt at a Solution If NN has a...

There is an interesting problem at MHF. I think I have an elegant solution for it, but the site won't let me post my reply. (It's only on this one problem. Go figure!) Anyway, I just have to share my solution. Add 2 to both sides: \:a^4 + 2 + \frac{1}{a^4} \:=\:121 \quad\Rightarrow\quad...

Hi, I'm doing further maths and I would like to study maths at university. I have been asked to read a number of books to put on my personal statement, and as I am finding it difficult coming to terms with the fact that mechanics is taught as maths and not physics, a maths don at Oxford...

Hi, I have a problem that I need to solve, it goes like this: Using the fact that the geometric mean of a collection of positive numbers is less than or equal to the arithmetic mean, show that if annual compound interest rates over an n-year period are i1 in the first year, i2 in the second...

Here are some papers on cosmology I wanted to share with you. What are your opinions about them? http://arxiv.org/pdf/1003.1528.pdf http://arxiv.org/pdf/hep-th/0610213v2.pdf http://arxiv.org/pdf/0903.3070.pdf http://arxiv.org/pdf/1403.5277.pdf http://arxiv.org/pdf/astro-ph/9310012v1.pdf...

I was thinking, and somehow I had this little "thought experiment" type thing relating to objects and the speed of light. (This is just my thoughts, I don't know if it's correct or the validity of my assumptions, etc) Imagine you're in a (large) room, and that the effects of friction, air...

What a great teaching opportunity! Why aren't more textbooks gears towards kids actual interests. Most problems are so dry. Include batman or Spider-Man and kids may actually be interested!

##C_0=\{f\in L^p: f(x)\rightarrow 0 ## as ## x\rightarrow infinity\}## This is an interesting subspace because it is the subspace of ##L^p## in which the momentum operator from physics is self adjoint. It seems that there should be more to be said about the importance of ##C_0## though...

Hello! I'm new to physicsforums, and actually I'm kinda new to physics in general. I've recently switched my major to physics in college and I absolutely love it; this is what I've always wanted to do! I would love to do some complex physics/calculus related projects, not really in the sense...

Hi all, I'm currently a student teacher. Next week I'm going to teach a lesson on universal gravitation to grade 11 students. It's the first lesson on the topic, so it will be an introduction and not too in-depth. I'm struggling with ways to make it interesting. I decided to start the lesson...

I'm studying physics in Edinburgh, UK, and I'm on my second year of four. I used to be passionately excited about studying physics at degree level but so far I've found it to be mostly uninspiring and often tedious. As stated in my title, I want to ask how usual it is to feel this way early on...

Lets suppose we have one dimension and in this one dimension we have two points.How can we symbolize both of them or I f we want to symbolize between these numbers what should I use. Example we have 10 and 5 and I want to symbolize in this numbers and make a equation.Well it means the...

Homework Statement This is a required analysis for my Physics II lab. We recorded the motion of an object oscillating on spring, and are asked to use the slopes of different graphs that we plotted using the data collected in lab in order to find the spring constant (k). Both graphs were...

http://arxiv.org/pdf/1312.7128v1.pdf

Here's an interesting limit I found the other day...\text{limit}_{\, \epsilon \to 0^{+}}\sqrt{\epsilon + \sqrt{\epsilon + \sqrt{ \epsilon + \sqrt{\epsilon + \cdots} } } } = 1It's both obvious and yet elusive... Any ideas on how to prove it...?

So while i was cooking my eggs this morning for breakfast, some interesting questions dawned on me. Are eggs a liquid or a solid and more interestingly, why do they become a solid when they are heated up? If eggs are a liquid, why don't they change into a gas? If they are a solid why don't...

1. Hello gentlemen! I've studying the Feymann lectures, and I came across an interesting question, from reading the chapter 6, about probability. In this chapter, Feymann deduces the binomial distribution, and I am ok with that. But, in the 3rd section, when adresses to the random walk problem...

Hello, whilst making my coffee this morning (more like this afternoon, but hey I'm a student), I noticed something that I thought was cool and I'm interested in hearing what you guys think may be happening and/or what you have to say about my ideas. So, I have these 'coffee filters' that are...

I am not sure where else to post this. Hopefully this is not in the wrong place. I am student teaching in a physics classroom this week. I will be teaching about scalars vs. vectors, calculating average velocity, and calculating acceleration. As I plan my lessons, I've realized they are...

I don't want to talk about interesting being a subjective quality but the main paradox. Since the first dull number is interesting, we classify it as interesting. But then the second dull number becomes the first dull number. So it is also interesting. But if we look again, we have two new...

Homework Statement \int\limits_0^\frac{\Pi}{2} \ \frac{x \sin x \cos x}{\sin^4x+\cos^4x} dx Homework Equations -- The Attempt at a Solution I first started to try a u-sub, then attempted a change of variables. I tried simplifying the expression, but the closest thing I came to...

I have the following problem, suppose we have a graph G of n elements, with the property that if we add one missing vertex v, we will get a complete subgraph with s elements K_s of G, in which v belongs to G'. In other words every subgraph of s elements of G is almost a complete graph except for...

okay, there are two curves: curve1: y=a^x and curve2: b^x. what is the angle between them at their point of intersection. given that (a≠b). My general method: if i wanted angle b/w the curves y=x^2 and y=(x-2)^2, i would easily do it. let A be angle b/w them...

For those unaware, geometric algebra is a mathematical language that generalizes and simplifies a lot of the tools physicists work with (vectors, complex numbers, tensors, etc). I found a neat example in classical mechanics to illustrate its power. Simply, a charge in a constant magnetic field...

Homework Statement A 160 g rope 4m long is fixed at one end and tied to a light string of same length to other end.Its tension is 400N. What is the wave length of first overtone? Homework Equations λ=v/f v=√(T/μ) μ=mass per unit length T=tension f=frequency The Attempt at a Solution...

Prove the following Euler sum \sum_{k\geq 1}\left(1+\frac{1}{3}+\cdots +\frac{1}{2k-1} \right) \frac{x^{2k}}{k}=\frac{1}{4}\ln^2\left( \frac{1+x}{1-x}\right)