Interesting Definition and 754 Threads

class. I did a lecture last semester on financial mathematics and stochastic processes. Know of any cool topics that I could lecture on?

I was making a PCB drilling machine at home with my brother, and came across this mathematical? problem. I needed to fix the drill machine. But I needed to determine where should it be fixed so that I could drill largest possible PCB boards. In other words, find the value of x so that you...

This whole unit thing of mols is somewhat tricky and interesting. if one mol of Na is 23g, then wouldn't 100.3g of NaCl be one Mol as well. I am under the impression from my lecture notes in class that the grams of a substance is the same a s a mol. I was asked a school of thought question by...

Homework Statement Suppose an elastic ball is set into projectile motion on an inclined plane, which makes an angle of 30 degrees to the horizontal. It is projected with an initial velocity of 5 m/s, making an angle of 20 degrees to the slope of the plane. Suppose the plane is very long, and no...

So, its a long post and I feel I've been pushing this thing further and further without considering it properly. Here's the background: I am doing a 5 year B. Tech. + M. Tech. Integrated course in Biotechnology and Bioprocess Engineering. There's one major issue though. My curriculum doesn't...

Today while working I found that an M6 x 1.0 Thread bold will easily screw into a hole tapped 1/4"-28. At first when I found this, I thought one of my boxes of bolts was labeled wrong, but I tried another set and it work. Has anyone else come across this similarity before? -CR

Hello and thanks for your consideration, I'd like some insight into the function f(\phi) = \frac {1 - \phi}{\phi - 1} Does this apply to any known modeling situations? Is it recognized as belonging to a more general class of functions that may have interesting or unique characteristics? Or...

Hi, I would like to know if anyone has good ideas for problems involving calculus of variations, other than the classic textbook questions (brachistochrone, Fermat, catenary, etc..) that I could create as a classical mechanics class project? Thank you

People have found ways to extend the definition of some operations that are ostensibly discrete (such as differentiation - e.g. 1st, 2nd, 3rd derivatives) to operations that are defined for fractions ( e.g. fractional derivatives). Is there an interesting way to extend the operation of...

Hello, Has anyone read any good or interesting Cosmology books lately? Thanks

I'm in the point of my life where I am about to be applying for universities. I'm completely unsure of what I want to do with my life, and I'm in a worrying frenzy. Now, the ever-so-controversial question: What is the most interesting, unique and fascinating major? I know it depends for...

Recently, my friend tested me on a puzzle. The puzzle goes like this, if there is 8 balls (1 of them which weighs either lesser or heavier), how are you going to find out which is the different ball using a two sided weight scale with 3 tries? This is a pretty easy puzzle which everyone would...

Can anyone tell me what this is? My son created it as an entertaining exercise -- he says it transposes positive integers. Is he right? \left(n\right)=\sum_{k=0}^{[log_b\left(n\right)]}\left(b^k\left(\left\lfloor \frac{n}{b^{\left\lceil log_b\left(n\right)\right\rceil}-k-1}\right\rfloor \%b...

Homework Statement You have been tasked with the design of a new far-field, high resolution imaging system to be placed on the Hubble Space Telescope. This system will be used for taking deep space astronomical images with an exposure adjustable between 10 minutes and 24 hours based on the...

For my research I am trying to solve a particular integral. I know that I have to transform it properly to use the residue theorem, but I am having difficulty attaining this form. Here is the integral: \int^{\infty}_{-\infty}\frac{e^{ix}dx}{\sqrt{a - x^2 + ib}} where a and b are real...

The properties arise from infinitely nested functions such as: x=\sqrt[n]{x^{n-1}\sqrt[n]{x^{n-1}\sqrt[n]{x^{n-1}\sqrt[n]{x^{n-1}...}}}} You can solve it algebraically to verify that x is equal to the nested function (all of the following functions can be solved in a similar manner)...

Hey, I'm starting a career of knowledge in the subject of physics. I'm so interested in it because to me physics is the language of the universe and to know anything at all is to start in physics. I am just curious of what part of the subject made you so interested in physics.

Just bored and looking for some new (<2 years ago) articles people find interesting. If anyone knows of any diseases that may be caused by neurological disorders which isn't proven yet, for example diabetes, they'd be a good start. Cheers

I have almost no idea how to start! I'm just doing this problem for fun(or was at one time): Find all a such that the equation x^2+axy+y^2=1 has infinitely many solutions in integers for x and y. I know that the solution of this problem would follow from a complete understanding of integer...

I saw a shadow of a catenary (or close enough) on a cylinder and wondered about the shape. Specifically, it was a powerline strung between 2 utility poles, and the sun angle would have been around 45 degrees or so, and the cylindrical grain bin was between and north (I am in northern...

I'm a senior in HS. Took AP Physics B last year had a 93 avg and got a 5 on the AP. Taking Ap Physics C this year. Started reading "The Fabric of the Cosmos" by Brian Greene and learning about astronomy over the summer. I really like this kind of stuff but the actual class, Physics B and C...

Looking for an interesting Mathematical problem "family" And what do I mean by that. All right, I think this was the most fitting category, I hope I'm not too off-topic. So I want to write a puzzle game, but, as everyone who loses his time playing puzzle flash games (like me), knows that you...

Perhaps it is known to you, it was something new to me. After Andy confirmed that reasonable circle of confusion for my camera should be about 0.02mm, I did some calculations - and I was surprised by the result. Say you have an object that you want to take a picture of (be it flower, book...

Interesting Telescoping Series -- Calc 2 My problem with this series arose when I attempted a partial fractions decompisition of the following, (k-1)/(2^(2k+1). I attempted to factor the denominator with 2(2^k) which is right, but where do I go from there? It does not help much to multiply...

Let A and B be two coprime integers. Find X = zero mod A such that Y = 2*X +1 = 0 mod B. Then 8*(Y +2*N*A*B)*(X + N*A*B) + 1 is a square for all integer N. If A = 5,B = 7, X = 10, Z = 21 then the sequence of square roots of the Squares for N = -3 to 3 is -379, -249, -99, 41, 181, and 321. Of...

Hi everybody, I'm a long-time reader and new poster. At the moment I am looking for some interesting Calculus of variations problems to present to 2nd year maths students. Naturally, I am already looking at the historical problems, The Brachistochrone, and I also have an applications of...

A natural integer N can be written as x mod p, for instance: N... 1 2 3 4 5 6 7 8 9 10 11 12 p=2 1 2 1 2 1 2 1 2 1 2 1 2 p=3 1 2 3 1 2 3 1 2 3 1 2 3 p=5 1 2 3 4 5 1 2 3 4 5 1 2 p=7 1 2 3 4 5 6 7 1 2 3 4 5 Etc. The puzzle is quite difficult to state in this format but I'll have a go: You...

3^3 = [3^3 - 3^2] +[3^2 - 3^1] + [3^1 - 3^0] + 3^0 Practical Demonstration: 27 = [27-9] + [9-3] + [3-1] + 1 27 = 18 +6+2+1 27 = 27 Is this property discussed in theory of games?

Hello, recently, I have found so called Batman graph and equation, which basically plots Batman sign. I have even found Python code that plots this implicit equation. Code can be found here: . And the equation is given here: [url]http://i.imgur.com/CNy9J.jpg If you look closelx...

Find the sum of : [2^{}0/3] + [2^{}1/3] + [2^{}2/3] + [2^{}3/3] + [2^{}4/3] + ... + [2^{}2008/3] where [] is the greatest integer function symbol... if the question is not clear here is the question.. Find the sum of : [(2^0)/3] + [(2^1)/3] + [(2^2)/3] + [(2^3)/3] + ... [(2^2008)/3]

I watched a video explaining a card trick today, there were no tricks, it was all based on math. Here's the set up: 52 cards in the deck. person A takes some of them, then person B takes some as well. The dealer counts the remaining cards in his hand, say he has 18. Then he says...

Homework Statement Find all x in |5x-2| = 6x-12 The Attempt at a Solution http://www.wolframalpha.com/input/?i=Plot[|5x-2|+%3D+6x-12%2C{x%2C-1.5%2C1.5}] Notice how only x = 10 is a solution? So my question is, why isn't x = -14/11 a solution? I mean sure they don't...

Mechanical energy against gravity? (Interesting energy problem) Why doesn't the above picture work? (I think it has to do with relativity, not 100% sure)

Given N= 1.2.3 + 2.3.4 + ... + n(n+1)(n+2), prove that 4N + 1 is a square (n is a positive integer)

Homework Statement http://www2.seminolestate.edu/lvosbury/images/VibSpringAnNS.gif Find the governing differential equation and position functions for a 32 pound object attached to the end of a spring with a spring constant of 1 and a forcing function that yields a constant velocity in the...

Homework Statement n2<=2n n is a natural number For what values of n is the statement true and prove by induction. Homework Equations The Attempt at a Solution I tried 1 and it worked, I tried 2 and it worked, just for fun I tried 3 and it didn't work, so I assumed the...

Homework Statement Find the acceleration of the system. Friction constant of incline is 0.2 Homework Equations Force of friction = 0.2 * 7 * 9.8 * cos30 = 11.88N Force of gravity pulling down 7kg weight = 7 * 9.8 * sin30 = 34.3N Force of gravity pulling down 4kg weight = 4 *...

Hey, my problem is that I really want to flirt with girls and have dates badly. However, when approaching a girls, I feel that I have no plan. If I start a conversation anyway, it might sometimes go OK in like the first 20 seconds, but then I end up not really knowing what to say. I know...

Find the area of the shaded region if r = 1/4 and each side of the square is 1. I know the solution can involve similar right triangles and systems of equations, but if I remember correctly this was a pretty messy way to do it. Anyone have a simple (or more complicated) solution? You can...

This is not a bookquestion by far. It does have a nice solution, but I am stumpled on how to get it \int_{0}^{\infty} 1 - x \, \sin \left( \frac{1}{x} \right) \, \text{dx} Now I could split the integrals into two pieces, where the first part obviously goes towards infinity. The second...

I just finished my second year of Engineering Physics at McMaster (specifically, nuclear) and I'm on a summer coop term now, but I'm looking for something fun to do after work and on weekends. Does anyone have some fun, interesting project ideas? I've got some experience with analog and digital...

Hi, Do someone have a clue on how to answer that? : An anomalous bright red spectral emission line has been detected in the nearby solar-type star GL1023. The brightness of the feature sometimes suddenly changes by a factor 2 with a frequency of 0.92Hz. After about 10 min of these...

Homework Statement Consider a translating and rotating rigid disk. As it movies, it just tips the top of a rod that is initially at rest. The puck sticks to the rod, forming a rigid body that looks like a popsicle that after the collision moves on as one rigid body. I did the calculations to...

Homework Statement The problem can be found here. http://wopho.org/dl.php?id=17&dirfile=selection-problem/helical_rope.pdf" I am attempting to solve part 3. Homework Equations The Lagrangian of the system is: L= \frac{m\dot{x}^2}{2}+\frac{mr^2\dot{\theta}^2}{2}-k \left(...

Homework Statement Consider the picture below. The picture below shows an infinitely long cylindrical line of charge with charge density per unit length +\lambda and it is located at the center of a non-conducting cylindrical shell with an infinite length and has a charge density per unit...

Hi Guys, What are the milled indices of plane (see attached figure). Its very interesting...and I am receiving every-time different answer from others. Have a look. Shriphy

Homework Statement If you could hypothetically experience 1 femtosecond (1E-15 s) the same way you do normally for 1 second, how long would it seem to experience 7.078E-4 seconds? Homework Equations note: 1 femtosecond is to 1 second, what 1 second is to 31.7 million years. The...

Homework Statement http://img687.imageshack.us/img687/9065/matrixk.th.png Uploaded with ImageShack.usThe Attempt at a Solution Alright, here is how I did it. First I need to find my eigenvalues \begin{bmatrix} 0-\lambda & 1&2 \\ 0& 3-\lambda& a\\ 0 & 0 &0 -\lambda \end{bmatrix} So...

Hello, I am faced with a perplexing challenge in analyzing my results for an ecology experiment. All help is immensely appreciated. The situation: I have 6-month longitudinal mass data for 8 hummingbirds. From eye-balling the data, time definitely has an effect: masses tend to decrease...

I find these problems difficult anybody want to help me out?