Interesting Definition and 754 Threads

Dear community I'm trying to get a grip on this integral: \int \frac{\sqrt{1-x}}{\sqrt{x}-1} dx. I tried substituting x=\sin^{2}(u), which leaves me (standing) with \int \frac{\sin(u)\cos^{2}(u)}{\sin(u)-1} du. But I just can't solve it, no matter which way I try. I would be thankful for every...

This project brings up an interesting legal dilemma with basic public key encryption and sharing digital copyrighted material: http://monolith.sourceforge.net/ ---------- Here is the basic gist: Let's say I have a copyrighted file that is represented by the following bit sequence...

I saw on this website http://www.fullmoon.nu/book/ A article about a Conversation with God that's the name of article. Its pretty interesting. Talks about god as a natural existence, http://www.fullmoon.nu/articles/art.php?id=tal this might be old here and sorry if it is.

OK, i built a computer for my step-brother today. After a lot of pain getting it to boot, i got it working. But in windows, the menu for safely removing hardware (like what comes up when you put a usb key drive in) comes up, and the main (only) hard drive is there. but in my computer, it...

Can anyone suggest ideas for interesting projects in Biology, preferably Botany. There should be some amount of practical work involved in it. It shouldn't go too complex like DNA fingerprinting, etc.

Two sides of a triangle have lengths a = 5cm and b = 10cm, and the included angle is \theta = \frac{\pi}{3}. If a is increasing at a rate of 2cm/s, b is decreasing at a rate of 1cm/s and \theta remains constant, at what rate os the third side changing? Is it increasing or decreasing? Just...

We had to do a question in my Advanced Mathematics class, and the way that I did the problem was supposedly right. My teacher even did it that way. However, the answer was wrong, so my teacher showed us the correct way to do the problem. The dilemma I have is that BOTH ways should work, but...

I wasn't sure where to put this thread... if it's in the wrong place, please move it. Anyways, I'm making a couple of posters for display and one of the showcases is featuing antique equipment like ohmmeters (Wheatstone bridge), ammeters, voltmeters, etc. I was wondering if anyone knew of any...

Hmm...well, it may seem rather immature :redface: Using any quantity of (any) halogen and SPONCH atoms, draw a molecule of the molecular solid possessing the highest \frac{\text{Melting point}}{\text{Molar mass}} ratio. (Note: Diamond is not a molecular solid; it is a network solid) What...

hi I'm currently in yr 12 in my first year of the IB diploma studying higher physics. i have chosen to complete my 4000 wrd essay in this subject, but i can't think of a suitable research question. The essay can either be a simple written essay or an investigation/experiment. i would like to...

This isn't homework, but I'll post it anyways because I'd like to know. It's from Herstein's Abstract Algebra. Show that if u = 4n + 3, where n\inN, then you can not write u in the from u = a^2 + b^2, where a,b\inN. I feel silly for asking this, but I'm curious to know. The one thing...

I was reading over my Physics book during break, what a shock huh, during my break? lol. Well I ran across two questions that interested me, they are not homework problem but I was curious about them. So I thought I would see if anyone knew the answers. So here they are. 1) Why are the frets...

Hey guys, u know how Euclid proved that primes r infinite. Now knowing that primes r infinite, if we take some primes p1, p2, p3,...,pn then will p1*p2*...*pn(+/-)1 always be prime?

Hey everyone, I have a free response question concerning some rather simple mechanics presented in a ratheruh...interesting way. We have a block of mass M, that slides don a hill at an angle of theita. the block slides down the hill from rest at s=0 to the final position/distance s. Here's...

I just finished reading this paper, and have a question: CAUSAL SITES AS QUANTUM GEOMETRY J. DANIEL CHRISTENSEN AND LOUIS CRANE Abstract. http://arxiv.org/PS_cache/gr-qc/pdf/0410/0410104.pdf We propose a structure called a causal site to use as a setting for quantum geometry...

Interesting question about probability. Someone could help me to find the answer ? "[FONT="Arial"]One bus arrives in the bus station between [12:58 am, 1:02 pm] and wait 15 seconds before to go out. One man arrives in the station bus between [12:59 am, 1:01 pm] and wait 30 seconds before to...

Pharyngula has some exerpts from Jones Dover school board decision that impressed me as well and truly written: http://pharyngula.org/index/weblog/comments/the_bottom_line_in_dover/ http://pharyngula.org/index/weblog/comments/unconstitutional_to_teach_id/ in case these links are slow (lot...

Hi everybody, I was wondering if anyone can suggest any really interesting math problem, as I seem to have reached a point where I am tired of reading theory and need to focus on some serious problem. I have studied Calculus 1 and 2(=single and multivariable calculus for Real numbers) ,some...

Interesting question - Not homework! Show that the sum of the infinite series: log_2 e - log_4 e + log_{16} e + {(-1^n)} log_{2^{2n}} e ... equals \frac{1}{ln2\sqrt2} Any ideas?!

I'm looking at an integro-differential equation prompted by a HW question. This is a simplified version of it: \frac{df}{dx}=-\frac{af}{x^2}\left(\int_{x_0}^x u^2f(u)du+M\right);\quad f(x_0)=1 with: x_0>0 and a and M positive constants. Does anyone know if it can be approached...

Here’s a question for you all… but first some background (see jpeg attachment for sketch) Assuming all surfaces are frictionless (5kg on horizontal surface, two 2kg blocks on 5kg block), and the pulley has no mass, with what horizontal force applied to the 5kg block will the two 2kg...

Do any of you guys have a favorite state? A least favorite state? Commentary to make about strange things you see in particular states? For me, I have to start off with three tidbits: 1) The I-40 in Arkansas is of less quality than clay roads I've seen on Indian reservations, so what the...

Hello, I am practicing for the INternational Physics Olympiad qualifier and I was working on a practice test when I stumbles across what seemed like an easy problem. I thought It was super-intuitive, but I can't seem to verify a correct answer with the multiple choice selection. Here's the...

The entire text is taken from the following website: http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html Has there ever been proven in practice that mass of an physical object/particle does indeed increase with its velocity? Here is the text copied from the website(written above)...

Let n be a positive integer and suppose f is continuous on [0,1] and f(0) = f(1). Prove that the graph of f has a horizontal chord of length 1/n. In other words, prove there exists x \in [0,(n - 1)/n] such that f(x+1/n) = f(x)

I saw Doom the movie last night and there was an interesting concept in it. They said that an artificial 24th pair of chromosomes was created to manufacture greater beings, they were basicly far more superior. And I thought, is this possible? Could chromosomes be added or change to make a...

Hello, everybody! I'm a Maths/Physics student at Ecuador. Sorry if my English sucks, i'll try to do my best... Some fellow Physics buddy asked me if there was a way to fin a complex number that would be equal to its exponential... it is a very simple question to understand, but not to easy to...

I am not too sure where to post this, but i suspect that it is mechanical so here goes... Not too long ago, i read a book about by Richard Feynman and came upon this puzzle. If you twist a metal tube to form a 'S' shape, then pivot the tube in the center. Next connect a water hose to the...

This man claims to have seen bigfoot, and he has drawn many pictures of it: http://www.fisheadtackle.com/Bigfoot.html I think the drawings are fun. http://www.fisheadtackle.com/bf-FACE992.jpg

I came across this puzzle a while ago and recently recalled it but couldn't come up with any solid solution/explanation. What are your thoughts? I want to choose one day, in a five day window (we'll say monday to friday), on which an event will occur. (For simplicity of interpretation and...

Interesting guy, what do YOU know?

Well, I'm in high school. I want to be a physicst but arent physicst engineers? I want to be able to use calculus and mathematics to design individuls computer parts, especially the chip CPU for portable gaming systems. Like the PSP, a marvel of technology I'm a senior in high school. Today a...

Very simple in writing, but hard to solve: x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2) :-p

In the HW section, someone proposed: u^2\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=0;\quad u(x,0)=x As per "Basic PDEs" by Bleecker and Csordas", treating this as: F(x,y,u,p,q)=0\quad\text{with}\quad \frac{\partial u}{\partial x}=p\quad\text{and}\quad\frac{\partial...

Hi, I didnt know where to exactly put this thread (since it is partially high-school related) so I put it here. Im in my last year in high school at the moment and want to learn some maths that you don't ordinarily do in high school - something offbeat or such. I am really not sure where a...

Hello all Genius people, how r u .This question might be easy for u but i am not able to solve this question.Can anybody of u tell me to solve this problem in detail.I will be very thank ful to u .please please solve in detail.i have spent 2 days just thinking about this question but i was not...

Hi, I am a grade 12 physics student and my teacher asked us the following question: You have a perfect balance scale, with two identical hourglasses on each end. They each have the exact same amount of sand in them. However, one (hourglass 'A') has all it's sand in the bottom, while the...

can anyone explain the behaviour of this function? i looked at the graph and everything, but if i solve it one way i get a different answer than if i solve it another way. Ln[(x+1)^2]=2 one way to solve it (What i did) e^{Ln[(x+1)^2]}=e^2 (x+1)^2=e^2 (x+1)^2-e^2=0...

I just received in the mail an unsolicited examination copy of The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics (2nd ed.), by George Greenstein and Arthur Zajonc (Jones and Bartlett, 2006 :bugeye: ). I haven't had a chance to do more than skim through it yet...

Hello, I tried to model and answer this question, but I didn't get success. Could someone help me ? Question: A California driver decides that he must switch lanes every minute to get ahead. If he is on 4-lane divided highway and does this at random, what is the probability that he is back...

From the Investment savingings model (IS) equation GDP (Y) is a function of consumption C, Investment I, and government spending G Y=C(y,r)+I(r)+G Consumption is a function of disposable income (income minus tax. national income is also the same as GDP) y which is y=Y-T and the interest...

This paper (with some actual math...surprise!) is in very close agreement with the polarized-ZPE model that I have been working on for a while. It treats gravity and inertia as emergent, not basic, qualities, and although it does not address the mechanics of vacuum polarization, I believe that...

http://www.windmillworld.com/uk/chesterton.htm http://www.roman-britain.org/places/chesterton_on_fosse.htm The wind mill over looks the roman fort site. With permission to search i have found roman coins around the mill. The site is about three miles across country from where...

A snake with a little more than 4 meters takes a walk for the forest in the following way. After to walk 1 meter in definitive direction it decides aleatoriamente if she capsizes for the left or if she capsizes for the right or if she continues in the same direction, independently of the...

Can someone help me? Why the argument is false ? In this problem you must explain the results in intuitiva way. One formal prove or verbal description of a prove is not satisfactory answers. 1) It considers the following events: A: To get one 6 in four throwing of a die; B: To get one...

How does one proceed to solve an equation of the form: a^x + x^b = c Where x is the unknown (real or complex) and a, b, c real constants. Or at least if you know a line of attack.

I've always been interested in unusual phenomena in conscious experience-- events in consciousness that are novel, surprising, sublime, or just plain strange with respect to the normal waking consciousness in which we are usually ensconced. In the interest of exploring this topic, I'd like for...

There is a theroy that universes "reporduce" through black holes, and that part of the criteria that requires this also by coinsidence produces conditions that make life possable. Discussion questions: What happens if two black holes merge? If intellegent life creats many tiny black holes...

One end of a rubber band with a length L is attached to a wall. The rubber band is held horizontally and the loose end is pulled away from the wall at a speed v, stretching the band. Simultaneously, an ant begins to crawl away from the wall along the rubber band with a speed u < v. Assume that...

! question... Why does lnX!=XlnX-X?