Interesting Definition and 790 Threads

Homework Statement Find the externals of the functional $$\int\sqrt{x^2+y^2}\sqrt{1+y'^2}\,dx$$ Hint: use polar coordinates. Homework Equations ##x=r\cos\theta## ##y=r\sin\theta## The Attempt at a Solution Transforming the given functional where ##r=r(\theta)## yields...

We know that the attractive force between the opposing poles of identical permanent magnets is a product of their field strength and that the total force diminishes as the distance between them increases. If we assumed the magnets to be point entities, the formulation is the same as that for...

Svein submitted a new PF Insights post Using the Fourier Series To Find Some Interesting Sums Continue reading the Original PF Insights Post.

Is there a way to predict what resins form solids based off certain hardeners.

Hello Forum, I am reviewing water and its 3 phases (solid, liquid and gas). a) At the triple point, water can be in the three phases simultaneously. Does that mean that for a certain amount of water, say 30grams, we would find, approximately, 10 grams of liquid water, 10 grams of ice and 10...

Hey, guys. There is something interesting about the skin effect, which also made me curious:wink:. Could you please help to solve it? The following is what I got from Wiki. It is said that, according to theory of induction, induced current would oppose the change of magnetic field. Then when...

Interesting and humorous lecture by Prof RP Feynman: http://www.cornell.edu/video/richard-feynman-messenger-lecture-1-law-of-gravitation The first few minutes capture Feynman's unique character.

I'm trying to decide which sort of engineering I want to do. I am leaning towards mechanical, what are examples of environments where mechanical engineers can work? Thanks.

Hi everyone. I wanted to post this interesting essay by Donald and Stuart Geman on Science in the Age of Selfies. http://www.stat.berkeley.edu/~aldous/Blog/PNAS-2016-Geman.pdf The essay raises some interesting questions on the scientific enterprise in the age of online communication and great...

https://www.physicsforums.com/threads/new-lhc-results-2015-tuesday-dec-15-interesting-diphoton-excess.84798 and status from Monday CMS released their conference note a bit earlier. They see absolutely nothing at the mass range where the excess appeared in 2015. It is a bit curious that they...

So I'm entering my second year in uni doing a physics degree. We're just about to tackle on some of the interesting topics like EM (which I've self-learnt before), Classical Mechanics(we've already covered Newtonian) and QMech. Apart from my core academics, I'm interested in pursuing some...

We build a special number from ##5##, by squaring it, appending the next digit of the square to it and repeating the steps. ##5^2=25.## The next digit is 2, which is added to 5 to give 25. ##25^2=625.## The next digit is 6, which is added to 25 to give 625. ##625^2=390625.## The next digit is...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on Chapter 4...

Starting in the fall of this year, I'm going to get to start my own year-long undergraduate research project. To summarize as briefly as possible: Resources Available: Our university has access to the SMARTS consortium's three telescopes: - 1.5m CHIRON telescope - 1.3m ANDICAM telescope...

I was drinking coffee at a roadhouse and looked out the window. I observed a lake and a cloudy sky. While I had the cup on my mouth and blew in it, naturally there was condensation on the glass (I wear eye glasses). When I looked out through the window I experienced something interesting. For a...

I have a fondness for the Moties from The Mote in God's Eye and it's sequel, The Griping Hand. They are a hierarchical society with a biological necessity to reproduce or die. This leads to incredible population pressure and resulting societal collapse. Being "trapped" in one solar system they...

I thought I'd try a new experiment. Post a few video's that you saw today that you think might be of interest to the PF community. I know we have here the "YouTube classics" thread and the new section with the science videos, but this is designed to be more specifically attuned to what videos...

Hello Physics Forums, After about one year of research and construction, I have nearly finished building a functioning inertial electrostatic confinement fusion reactor. Just to be clear, I do not wish to discuss the dangerous activities that are involved with my project as I know such topics...

Hello! I am new to this forum so I don't know if I am posting this under the right part. Anyway, I am an undergrad and my phys 101 mechanics course requires to come up with an experiment related to the course content, write a report on it and present it to TAs. I decided on a simple pendulum...

I'm looking for examples of some interesting compounds that contain alcohol functional group (please, no joke suggestions about various liquor). Bonus points for creativity/thinking-outside-the-box. Thanks.

I would like to think about some interesting problems or interesting theorems to which one could find a proof. If you should know any I would be delighted if you could share them. Thank you very much.

What makes physics interesting to physics majors (ik this is kind of general)? Also how could I get interested into physics.

Hi all, just curious. I am just learning about user-defined functions in MSSQL2014. What kind of Math can we do with it? Didn't get much useful from my search.

You're in a Mars Lander. The planets gravity pulls you towards it at 3.711 m/s². (So at T(1) with 0 thrust your vertical velocity is -3.711). Your lander has 4 thrust settings: 0 m/s², 1 m/s², 2 m/s², 3 m/s², 4 m/s². Each of these use 0, 1, 2, 3 and 4 units of fuel per second respectively. Your...

this ice formation occurred with temperature hovering near zero C. It looks like something that was made in a mould! I suspect that a combination of winds and pressures caused by growing ice crystals in the plastic bucket tilted some crystals which continued to grow. I

I'm trying to understand why timelike geodesics in Anti de-Sitter space are plotted as sinusoidal waves on a Penrose diagram (a nice example of the Penrose diagram for AdS is given in Figure 2.3 of this thesis: http://www.nbi.dk/~obers/MSc_PhD_files/MortenHolm_Christensen_MSc.pdf). Bearing in...

Homework Statement I found this question and thought the situation was quite an interesting one.[/B] Homework Equations Seem to only be the 3 general equilibrium form of equations. The Attempt at a Solution The problem I encountered with this question was that when I isolated 2 or 3 members...

Skip to the good stuff at 1:41 and 1:52 and anywhere you see paint, can't embed link at the right time. Note the entire speaker flexing at 1:42 (slow both links down further if you can).

Hello,every one I am now a Phd student on particle accelerators in China. My tutor's interest is on more engineering things like machine design and running, but I'm tired of arranging magnets. I want to do more research on new physics ideas instead of becoming one doing machine designs...

I've been working on my SR book http://www.lightandmatter.com/sr/ and its presentation of a suite of related mathematical tools such as the Levi-Civita tensor. This is aimed at the upper-division undergraduate level, although there are optional sections at the end of some of the chapters that go...

After a slow start, the LHC and its detectors worked nicely and collected a lot of data this year (~3.5/fb). While many analyses are still ongoing, both ATLAS and CMS will report several results on Tuesday 3 pm (CET)*. The presentations will probably appear here, a...

Well, the tittle is self-explanatory. If anyone has an interesting problem or puzzle. I will be grateful if you could post it.

What with college essays and things these past few months, I've been a bit physics starved. I am looking for some interesting physics( and mathematics) problems to get my brains physics side whirring again. So please, fire away!

Hello, So I was asked this question the other day and don't really know how to go about it: "Define a random process by: Xn+1 = Xn+1 with probability 1/2 Xn+1 = 1/Xn with probability 1/2 Given that X0= 100, find the expectation of X10 " I've only ever really met random processes...

I am not sure if this fits under this title, but oh well... I guess it goes for students but also for higher in hierarchy people (they also like some problems which can have an extension) What has been your favourite to talk-about problem in Electrodynamics ? I am looking for something that...

Let $a_n$ be the $n$th term of the sequence $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, ...,$ constructed by including the integer $k$ exactly $k$ times. Show that $a_n=\lfloor\sqrt{2n}+\frac{1}{2}\rfloor$. (Hints only as this is an assignment problem.)

From time to time I hear about people coming up with creative/"non-mainstream" solutions to classical physics problems, whether by looking from a very different angle or using some unusual math that's unknown to anyone but that one slightly quirky professor from faculty of mathematics. However I...

can anyone tell me which is the most interesting field in physics .

Homework Statement For reference, this is the image setting up the problem. "A wireless sensor grid consists of 21×11=231 sensor nodes that are located at points (i,j) in the plane such that i∈{0,1,⋯,20} and j∈{0,1,2,⋯,10} as shown in Figure 2.1. The sensor node located at point (0,0) needs...

I know that most of you have grown up in this digital era, but me myself, I am a old school man, and, I usually use reference books. Today, I would like to recommend a small and practical book. Have you ever been working in an installation, in the middle of the Amazonian jungle or in the...

Homework Statement CH2=CHCHCH3 + X --> CH3CHClCH2CH3 CH3CHClCH2CH3 + KOH(aq) --> Y then what is the structural formula of Y ?? (show clearly where the functional group located)The Attempt at a Solution It is obvious that X is HCl, and Y should be an alcohol but where is the hydroxyl group be...

This isn't too much of a question, but more of an open proposal. Now... to begin, I know that both you, reading this, and I can agree that our universe is expanding. The universe is expanding from every point within itself, there is no Defenitive reference point, this is a fact. So for an...

http://arxiv.org/abs/1508.04641 The body text of the paper ends up calling the "Hybrid metric-Palatini gravity theory" f(X) gravity. From the body text (citations and internal references omitted without notation): The paper closes by identifying many issues for further study and arguing...

Hello everyone, I am a Physics education major in the Philippines.I am now on the stage of doing an undergraduate thesis as a requirement for my degree. I would like to ask for suggestion out there, for an interesting topic to be considered. I would really appreciate topics that gives a little...

Hello, I'm looking for some book of common (real) life or interesting problems, which are presented and scientifically sloved. I don't preffer any problem, but I mean some from real life, fridge, gyroscope, atc. Do you know any book of these problems and solution?

Hello all! I am currently taking a six week Calc II w/ Analytical Geometry and will be taking Vector Calculus in a few weeks, also six week course. I am a math major and I love math, but I find calculus a tad on the boring side. We just started infinite series this week, a little more...

Hi All, Recently, in my earlier thread, I asked about the symmetry of Lorentz Factor (where +V == -V). I had several pointers about how to handle this (Thank you all those). However, it seemed unanimous that there was no explanation beyond the equation itself (math or physical). Also, I...

I have some question about referance frame 1-Is physics works without referance frame ? 2-Is Space-time itself can be a referance frame ? I mean "Earth speed, relative to arbitary point in space time, is 100.000 km/s" Is this sentence make sense to physics ? Or we need an object to make a...

Here's an article by a woman who obtained a radiation monitor and noted it's readings at various places she went: http://www.ratical.org/radiation/radMonData.html I have a question about this passage: Why would this clock be so radioactive? I am also baffled by this revelation: Why is it...

So, I like proving theorems in number theory and calculus. I'd like some interesting ones to prove. Recommendations?