Points Definition and 1000 Threads

This might be more of an algorithm question than a math question: how do I go about distributing n points as evenly as possible in a 3D volume of non-basic shape? Think human organs or the like. A related question is how do you know when you're inside a 3D volume versus outside it? Thanks!

Homework Statement Determine the location and type of all critical points of the given equations and sketch the phase portrait y"+cosy=0 The Attempt at a Solution I've done some like this before but they were all systems of equations. I'm actually not sure how to do the...

I'm trying to teach myself optics from Frances Sears' book Optics from 1949. I'm attempting every problem, and there are answers to the odd ones in the back. I've gotten a lot of wrong answers and don't know why, had a few I just couldn't even see how to start, and at this point, I'm seeing...

Homework Statement I was wondering if you could help me on how to draw these on a graph (4, 0°) and (3, 27°) The Attempt at a Solution Just a hint, Please

I couldn't get these lines from my book. I will reproduce it here. Warning: In step 1, if you use computer to fit a polynomial to the data , it could lead to disaster. For example, consider fitting a sixth degree polynomial to the seven data points, or, an (n-1) degree polynomial to n...

Homework Statement The line that is normal to the curve x2+2xy-3y2=0 at (5,5) intersects the curve at what other point? 2. The attempt at a solution I differentiated the equation, found the slope of the curve at that point, and I then found the equations for the tangent line and normal...

So I am solving for the critical points of x3-3x-y2+9y+z2 I've found the critical points and I'm just evaluating them in the Hessain. Now I computed the eigenvalues for the hessian, but one of my 2nd order derivatives was a constant. So my hessian looked like this (it was diagonal, so I'm...

What is the mathematical equation or algorithm for alignment of four points in cartesian coordinates (X & Y). Say, we have 4 nominal points (Xn & Yn), and another 4 measured points (Xm & Ym)?. After alignment, what are the new locations of the measured points (Xmn & Ymn)?.

Hi, I have faced the following question. In our lab we perform different measurements on Transistors. We program a scope and that controls the tests. For one of our tests we would like to calculate the total charge Q. Mathematically this is given by Q=∫ dt i(t), where i(t) is given by i(t)...

I have the equation (x^2)/(sqrt(x+1)) This one has been stumping me, not sure how to reduce the derivative properly much less solve for 0. I get it down to this using the quotient rule: ((x+1)^(1/2)*2x - x^2*1/2(x+1)^(-1/2)) / (x+1) Just started learning derivative a few weeks ago...

Fitting points to "skewed" sinusoids Hello, I have a problem related to least square fit of data. Let me start from a step back. I have a set of points, given as x-y coordinates. x represents an angle and y the corresponding value of a function. I am fitting sinusoids to those data points...

Hello, I'm trying to find a good reference for how to find or calculate or know which points in the Brillioun zone are "TRIM" (time reversal invariant momentum) points? If anyone is familiar with this topic and could perhaps post a reference or two it would be of great help. Thanks!

My question is mainly concerned with discovering the allowable set of "configurations" of the given problem: We have a two-dimensional board composed of three sets (of infinite size) of parallel lines \P_1, \P_2, \P_3, where the lines in \P_2 form a 60 degree angle with lines in \P_3 and \P_1...

Why is the electric field strong in sharp points?? There is a question in my book regarding the intensity of the electric field near a sharp surface in a conductor. There is a hint which says that it will be helpful to examine the field lines near those sharp surfaces. This is from my...

Let f(x,y) = x^2 y - xy = x(x-1)y be a polynomial in k[x,y]. I am looking for the singular subset of this function. Taking the partials, we obtain f_x = 2xy - y f_y = x^2 - x. In order to find the singular subset, both partials (with respect to x and with respect to y) must vanish. So...

Homework Statement Basically I found the following system of DE's: \frac{dx}{dt}=y \frac{dy}{dt}=-\frac{g}{l} \sin x - \frac{cy}{ml}. (Damped pendulum) I'm asked to analize the stability of the critical points x=0, y=0 and x=\pi, y=0. Using intuition the first point is asymptotically stable...

Hi all! I need help..:) I need to model the dynamic of this system: I'm in the plane (2-dimensions). There are two points (with m1 and m2 masses) free to move with different speed vectors (in module and direction). At some point, when the distance between them is d, the two points...

Homework Statement Find a parametrization of the equation of the line formed by the points A, B, and P. A(2,-1,3) B(4,3,1) P(3,1,2)Homework Equations x=x_0+v_1*t y=y_0+v_2*t z=z_0+v_3*tThe Attempt at a Solution Alright, so, I've already determined that P is equidistant from the points A and...

1st part of Exercise #27 is: Define a point p in a metric space X to be a condensation point of a set E in X if every neighborhood of p contains uncountably many points of E. Suppose E is in R^k, E is uncountable and let P be the set of all condensation points of E. Prove P is perfect...

Homework Statement Plot the Following points(given in polar coordinates). Find all the polar coordinates of each point. a. (2, pi/2) b. (2,0) c. (-2, pi/2) d. (-2,0) Homework Equations none The Attempt at a Solution I have plotted it on a graph but could someone explain to me...

what creates the "star points" in telescope pictures of stars? it's a basic question. e.g. see this hi-rez Hubble Deep Space pic: http://upload.wikimedia.org/wikipedia/commons/9/9b/Hs-2004-07-a-full_jpgNR.jpg i count about three bright objects with pointy cross-like projections from...

Homework Statement Find all critical points of u(x,y)=(x-y)(x^2+y^2-1) Homework Equations - The Attempt at a Solution Partial differentials: ux=3x^2+y^2-1-2xy=0 uy=-x^2-3y^2+2xy+1=0 I know the critical points are the solutions to the above two equations. But how do...

Homework Statement Locate and classify the critical points of f(x,y) = (x-y)(xy-1). Homework Equations The Attempt at a Solution I found the partial derivatives with respect to x and y and I got: ∂f/∂x = -y2+2xy-1 ∂f/∂y = x2-2xy+1 After setting them both equal to zero I can't...

Homework Statement Find all points C on the line through A(1, -1, 2) and B(2, 0, 1) such that vectors llACll= 2 llBCll Homework Equations Not sure. The Attempt at a Solution I found the equation of the line for vector AB: (1,2,-1) +t(2,0,1) Then found the scalar equation...

The point P(4t^2, 8t) lies on the parabola C with equation y^2 = 16x. The point P also lies on the rectangular hyperbola H with equation xy = 4 a) Find the value of t, and hence find the co-ords of P. working: so x = 4t^2 and y = 8t i sub these into xy = 4 and get t = 1/2 and can then...

Homework Statement I am confused here . Each wire is of resistance R How in this image E G and D are at the same potential and in this image How A and F and Dand G are equivalent? Homework Equations I don't think any equations will be used in solving this but I guess V =IR might be...

Homework Statement The question is to find Equivalent resistance between opposite ends of a cubical resistor network . each resistor of resistance R . I am referring to this website here http://mathforum.org/library/drmath/view/65234.html I am halfway through it but I am stuck at a...

By Peano's space-filling curve, there exists a continuous map f: I -> I^2 whos image fills up the entire square I^2 (where I=[0, 1]). This can also be represented by gluing points of I together. Which points of I get glued together? I was looking at the proof of Peano's space-filling curve...

Homework Statement Triangle A has three points a(2,3)b(0,0)c(2,0) and its center is (2/3,1). Find the other three points of Triangle B with a center of (4/3,3). Homework Equations Center of a triangle: x = ax+bx+cx /3 y = ay+by+cy / 3 Magnitude = <a,b> , √(a^2+b^2) The Attempt at...

There is a theorem for finite groups of isometries in a plane which says that there is a point in the plane fixed by every element in the group (theorem 6.4.7 in Algebra - M Artin). While the proof itself is fairly simple to understand, there is an unstated belief that this is the only point...

Hi, I really need some help here. Right now I am plotting points on a 3D Scatter plot chart in Mathematica. I want to assign each of these points with a value which will be the label. Basically each point has 4 variable in the parameter. Its x,y,z cartesian coordinate position and the last...

Hi, i have three points A',B',C' and want to find a vector passing through B' and parallel to the other two points in the plane containing these 3 points. So this how i started, A'=(9,27,-0.6) B'=(12,27,-6) C'=(19,25,-8) I found the vector AB' and AC' first. A'B'= A'-B' A'C'=A'-C'...

Hey, how do I determine whether or not points lie in a straight line? Is there a symbolic approach to determining so? Or do I need to spatially visualize it? For instance, A(0,-5,5), B(1,-2,4), C(3,4,2) does lie in a straight line according to my book. Thanks!

Homework Statement I am trying to find the critical points of the following hyperbolic function: f(x) = a / (b + x) Homework Equations Critical points--> where f '(x) = 0 One of the points on the graph is a/2b The Attempt at a Solution I am not sure how to proceed with this...

Homework Statement f(x,y)= 16(y^2) +(x^4) y + 4(x^2) + 4 My problem is recognizing which critical points to consider valuables. Homework Equations fxx, fyy, fxy, and second partials test. D=fxx(fyy)- (fxy)^2 The Attempt at a Solution I found: fx=0 4(x^3)y +8x=0 (x^2) y= -2...

Hello, I am no mechanical engineer and my knowledge in bending is limited to Euler-Bernouilli beam theory. I wish to analytically calculate the normal stress of a plate bent by four points bending. I have already calculated this stress for a beam. However I cannot apply the beam theory...

The problem is: A, B, C, D are any four points in space. If M and N are the mid-points of AC and BD, show that AB + CB + CD = 4MN. I'm not quite sure where to start. Could someone please help me?

Homework Statement For each part, find the cartesian equation of the plane through the given points. (1,0,3), (2,-4,3),(4,-1,2) The Attempt at a Solution No attempt. Dunno how to do :(

Hi I have a set of data points in units of (time, voltage), and they have the form of a Gaussian when I plot it. I would like to normalize my data set, i.e. find a factor C that I multiply on to the voltage-data such that the area is 1. However, is there a way to numerically integrate data...

Homework Statement http://img444.imageshack.us/img444/9288/51927159.jpg The Attempt at a Solution (a) I'm mostly stuck on this part because I keep getting a complex number: 3x+y = 0 so x=-y/3 Substituting this in the second equation: \frac{y^2}{9} +1 = 0 \therefore \ y = \sqrt{-9}...

Critical Points, intervals, local max/min help! Calculus. 1. I need help with a homework problem that I just cannot get right. It asks: Answer the following questions about the functions whos derivative is given below. f'(x) = (sinx +1)(2cosx +\sqrt{3} ), 0\leqx\leq2∏ a. what are the...

How do we prove that the gradient points in the direction of the maximum increase? Would it be enough to simply state that the gradient is just the derivates of a function w.r.t all the variables a function depends upon. Since the derivative of a term w.r.t a certain variable gives the maximum...

Q.In which of the answers below are the substances listed in order of increasing melting point? a) Cl2 < CHF3 < H2O < CHCl3 < SiO2 b) Cl2 < CHCl3 < CHF3 < H2O < SiO2 c) Cl2 < CHF3 < CHCl3 < H2O < SiO2 d) Cl2 < H2O < CHF3 < CHCl3 < SiO2 e) SiO2 < H2O < CHCl3 < CHF3 < Cl2 How can we tell...

Homework Statement We are given the curve y = (1+x)/(1+x^2) Homework Equations y' and y'' The Attempt at a Solution I know the inflection points of y are the local minimum and maximum of y'; this can also be restated as the critical points of y''. My attempt is to find the...

Homework Statement Use the Cauchy Riemann equations to those points whose functions are analytic ##f(z)=x^2-y^2-x+iy(2x+1)## Homework Equations C-R eqn's ##u_x=v_y, u_y=-v_x, z(x,y)=x+i y## The Attempt at a Solution ##u(x,y)=x^2-y^2-x## ##v(x,y)=y(2x+1)##...

Hi, I am in honors track Complex Analysis, and I think I've reached my limit. We got this proof, and I don't know where to start. "We saw in class that a mobius transformation can have at most one fixed point (or else is the identity map), extend this idea to all analytic functions mapping...

Homework Statement Find the points x^2 + xy + y^2 = 2 that are closest to the origin.Homework Equations Distance FormulaThe Attempt at a Solution I have to first solve this without using Lagrange Multipliers. This is essentially an ellipse. So I first completed the square: 3/4\,{x}^{2}+...

Dear Folks: Suppose \Gamma is a discrete subgroup of SL2(R), which acts on the upper half complex plane as Mobius transformation. F is its fundamental domain. If z is a vertex of F which does not lie on the extended real line ( that is R\bigcup\infty ) ,then must x be an elliptic point...

Homework Statement Find the equation of a circle if the circumference is 18∏ and contains the point (2, 8) The Attempt at a Solution I know I can find the radius by setting 18∏=2∏r. r=9. the equation of a circle is (x-h)2+(y-k)2=r2 So I have 92= (2-h)2+(8-k)2 which becomes...

Is there a theorem that states that n distinct points in R^n-1 or higher one can be separated in an equal distance as the distance is greater than 0? We know that 4 distinct points in R^2 cannot be positioned in an equal distance>0 but in R^3 it is possible as a pyramid shape. If there is...