3d Definition and 1000 Threads

Thanks to those who participated in last week's POTW! Here's this week's problem. ----- Problem: Show that \[\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2}e^{-(x^2+y^2+z^2)}\,dx\,dy\,dz = 2\pi\] (Note that the improper triple integral is defined as...

Hi all, Can someone please help me, I am new to Matlab and I would like to use the following upload to create a 3d surface plot. I download all the files from: http://www.mathworks.co.uk/matlabcentral/fileexchange/28177-3d-surface-plots-from-excel-data-gui Then I open the MainGUI.m file...

u = unit of distance. Take a solid cube of dimensions (1u,1u,1u) with center at (0,0,0). Cut it straight along x, y and z three times with a circle of diameter 1u parallel to the faces of the cube with the center of the circle at (x,0,0), (0,y,0), (0,0,z) respectively, removing the "shavings"...

I have two triangles in 3d. I need to calculate transformation matrix(3X3) between two triangles in 3D. 1)How can I calculate the transformation matrix(rigid) while fixing one of the points to the origin(to get rid of the translation part)? 2)How does it affect if the deformation is non rigid?

Are the orbitals circular or spherical or parabolic?? Are they 3D? Are the orbitals circular or spherical or parabolic?? Are they 3D?

Why are there two versions of 3d in the theaters? What's the difference between them?

Does anyone know what compounds make up the resin used by resin type 3D printers? I need to know if it could possible react with some hexane, toluene, and other chemical solutions for sure, though I believe the resin to be fairly inert chemically. Thanks PF.

Homework Statement The system is a rectangular box with dimensions of 3 ft x 4 ft x 2 ft. There's an applied couple moment of 600 lb-ft on the x-z plane rotating positively. The moment is 2 ft above the x-y plane in the positive z direction. Applied force 1 is 450 lbs in the negative x...

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...

From my Math Textbook Suppose Romeo is serenading Juliet while she is on her balcony. Romeo is facing north and sees the balcony at an angle of elevation of 20 degrees. Paris is observing the situation and is facing west. Paris sees the balcony at an angle of elevation of 18 degrees. Romeo and...

hello EveryBody, In the 3D Coordinates I always find 4 parameters instead of 3. A = (X, Y, Z, 1) I wonder why? thank you.

Dear all, I am a medical doctor stuck with a mathematics problem. I have taken a project to map the 3D movement of a particular bone and describe its motion. My maths knowledge is a bit lacking. However using logic I felt that I would need to track 3 constant markers on the particular bone...

Homework Statement Find the volume of the solid inside the surfaces x^2+y^2+z^2=1 and z=x^2+y^2Homework Equations With x=0: z=y^2 ; z=√(1-y^2) or y as a function of z then gives: y=√z ; y=√(z^2-1)The Attempt at a Solution First, I attempted to sketch a cross section of the region by setting...

Hello, I have a 3D complex vector k=[k1,k2,k3], and k1, k2, k3 are complex numbers respectively. Now, I want to rotate k to a new vector t=[1 0 0]. However, I do not know the mathematical expression of rotation matrix. What is the difference between rotation in real domain and rotation in...

Is there any good software which plots 3d graphs and vectors. I just want to plot linear 3d graphs and vectors in 3d. I don't mind paying for this but it should be reliable and easy to use.

hello guys, I have a CSV file with hyuge set of data devided into 3 cols. Y position X position and corresponding intensity values. I want to plot the image , my thesis is laser- microscopy. so a 2D plot ( density plot ) based on these values. The following is what I have tried so...

I have a question about rhombic dodecahedra - polyhedra which can be tiled indefinitely, and which correspond to the closest packing of spheres. A single rhombic dodecahedron can be surrounded by 12 rhombic dodecahedra, making a tiling of 13 (having no gaps or holes or cracks). This creates a...

Homework Statement Problem as given: A three-dimensional wire of infinite length carries a current I0 starting at (-∞,0,0) along a straight line to (0,0,0), bending and traveling along a straight line to (0,1,0), then bending and traveling to (0,1,1) and finally bending and traveling out to...

The Green's functions for a 3d wave are like δ(r - ct)/r -- so if you have static source at the origin that is turned on at t=0, you get an expanding ball around it of radius ct, with strength 1/r. If you look just at the XY plane, you see an expanding disc of value 1/r. Similarly, if you...

What's it called when a 3D shape can be made of 2D surfaces of all the same shape and dimensions? To make a cube, I can use 6 4-sided-squares (of course they're 4 sided) To make a pyramid (3 sided), I can use 4 3-sided-triangles I can do this with pentagon as well (i don't know what the...

Hello! I tried to develop equations of motion of system of wheels, where the first one with radius of r is rotated with some angular velocity v, the center of the second wheel is connected with the first on its perimeter and its plane of rotation is perpendicular to the plane of rotation of...

Homework Statement Problem 15.18: I've defined the positive J (fixed) axis along the pole pointing upwards and the positive X (fixed) axis going to the right, with both centered at the point of contact between the hoop and the pole, which I will refer to as point O. The rotating axes...

If I consider the problem of for example the hydrogen atom. I.e. a central force problem with an effective potential V(r) that depends only of r, the distance between the positively charged nucleous and the negatively charged electron. In the Schrödinger's equation, one considers the...

does anyone know an easy to use 3d plotting software with vectors? i have been using maple for some things but 3d plotting vectors and transformations is really slow in maple. i really like geogebra but it can only do 2d vectors. any suggestions?

I want to plot a 3D graph. A solid graph and a wireframe mesh graph. What are the different ways to do it in this script. The variables i want to be plotted in this script are 'pic' 'TSFC' 'NonFs'. Dont mind the working, everything is correct. The only matter of concern is the 3d graph and...

Hello, I'm currently conducting a very serious high school research project titled: Maximizing Energy Efficiency of a Linear Electromagnetic Accelerator I have recently been bestowed with a temporary license for a very advanced 3-dimensional electromagnetism simulator that should allow me...

Let's say you have four points that define a rectangle in the xy plane centered at the origin (with the x,y axes bisecting the sides). How can you transform these points so that the rectangle lies in an arbitrary plane (defined by a point p and a normal vector n) so it is centered about point p...

Homework Statement Find the mass of the surface of the triangle with vertice (2,0,0), (0,2,0), (0,0,1) if the density is 4xz Homework Equations The Attempt at a Solution I know I just need to take the integral of 4xy in the region of the triangle, but how do i set up the integral...

The following is FreeMat code, but it should get you close enough in pure Matlab: --> x=[0:0.1:1]; --> [X,Y]=meshgrid(x); --> Z=X.*(X>=Y)+Y.*(X<Y); --> surf(X,Y,Z); CB

I am fairly new with simulink and only went through a couple of tutorials on how to use it. but i am looking to do some control system design with a 3D model. I know i have lots to learn so i would like to get some directions as to where i should go to reach my goal. I am looking to...

Homework Statement I have to derive Newton euler equations of an inverted telescopic pendulum with two links. I will use this model to simulate biped walking. The leg link is assumed to be massless and it carries the body link. The model at final stage should be 3d. In 3d case the hip namely...

I'm building a simple 20:1 gearbox prototype with 2 compound gears in a row connecting to a third small gear at the end. My goal is to multiply the rotational speed of the small gear. They are all engaged on a straight line. But for some reason they get stuck most of the time. I'm trying to...

Hey guys girls and thanks in advance (Sorry if this post is in the wrong area) Ive been working with splines in 2D for a little while now and am fluent with the mathematics behind them. I now need to use 3D splines but cannot come across a good reference material to reconstruct them ...

If I have a cylinder with a radius r and an axis that passes through point b with the direction of vector n, show that its equation can be written in any of the following forms: 1) ||(p-b) X n|| = r 2) (p - b) X n = r.e (where e s ia unit vector orthogonal to n) 3) ||(p-b) - ((p-b).n)n|| =...

Hi, I have a vector function (momentum \vec{p}(x,y,z)=\vec{p}(\vec{r},z) for \vec{r}=(x,y)) and need to transform it, also I use the Fourier transform F(\vec{p})=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \vec{p}(\vec{r},z) exp^{i \vec{\chi}\cdot \vec{r}}d\vec{r} and then when I have...

If I have a cylinder with a radius r and an axis that passes through point b with the direction of vector n, show that its equation can be written in any of the following forms: 1) |(p-b) X n| = r 2) (p - b) X n = r.e (where e s ia unit vector orthogonal to n) 3) |(p-b) - ((p-b).n).n| = r...

Homework Statement Given |\vec{a}| = 8, |\vec{b}| = 9 and the angle between vector \vec{a} and \vec{b} is 48° find the cross product, \vec{a} X \vec{b}. Homework Equations Let θ = angle between \vec{a} and \vec{b}. \vec{a} . \vec{b} = ( \vec{x}1 * \vec{x}2 ) + ( \vec{y}1 * \vec{y}2 ) + (...

Homework Statement A particle in a 3D cubical potential well. The walls are Lx, Ly, Lz long. Inside the well, V(x,y,z)=0 when 0<x<Lx, 0<y<Ly, 0<z<Lz. V= ∞ elsewhere. Solve the TISE to find the eigenfunctions and eigenvalues of this potential. And to normalise the wavefunctions. (Hint: look...

Homework Statement Good day to all. I have been given a problem in statics and a system in equilibrium which in turn is giving me some problems. I have attached in a pdf file the problem context as well as my attempt at a solution. I have done so, because I was experience some problems with...

what are the different ways to write four quantum numbers that designate an electron in a 3d orbital

Homework Statement The goal of this exercise is to plot parametric equations so that the image looks like the Agnolotti Pasta shell given in the link below. http://www.nytimes.com/interactive/2012/01/10/science/20120110_pasta.html?ref=science. Homework Equations The relevant...

Hi guys, I am looking for a simple 3D drawing program, where I could draw a bunch of balls of different colors and maybe some bulky arrows. If I could make a small movie (or a GIF) by making the balls move, that would be a nice extra. What would be the simplest solution? Mathematica...

Homework Statement Calculate the Fourier transform of f(x) = (1 + |x|2)-1, x\inℝ3 The attempt at a solution As far as I can tell, the integral we are supposed to set up is: Mod note: Fixed your equation. You don't want to mix equation-writing methods. Just stick to LaTeX. $$\int...

Yes, that is my problem. I could never reproduce in computer the scheme I learned in Computer Engineering graduation I am coursing. The way the teachers show and in some books, I never get into that result but I don't know if it is exactly impossible. At this page in wikipedia...

By continuity I mean an unbroken fractal. With certain variants, one ends up with sharp gaps in the fractal. mag=({x^2+y^2+z^2})^{n/2} yzmag=\sqrt{y^2+z^2} \theta= n *atan2 \;\;(x + i\;\;yzmag ) \phi = n* atan2\;\; (y + iz) new_x= \cos{(theta)}\;*\;mag new_y=...

Homework Statement Show that |\tilde{I}(\vec{k})|^2\leq CP^2 Where C denotes a constant, Using this inequality: \int f(\vec{r})^*g(\vec{r})\,\text{d}\vec{r}\leq \int f^*f\text{d}\vec{r}\,\int gg^*\text{d}\vec{r} Where k denotes the Fourier transform from r->k(in 3d) R is assumed positive...

Homework Statement What are the degeneracies of the first four energy levels for a particle in a 3D box with a=b=1.5c? Homework Equations Exxnynz=h2/8m(nx2/a2+ny2/b2+nz2/c2) For 1st level, the above = 3h2/8m For 2nd level, the above = 6h2/8m For 3rd level, the above = 9h2/8m For 4th level...

Homework Statement The system is made of a disc the center of which is pinned to the origin (so the disc cannot translate), and some weights that can be stuck on the disc to make it tilt (weights do not translate on the disc) (see images attached). There is no friction whatsoever. The only...

The system is made of a disc the center of which is pinned to the origin (so the disc cannot translate), and some weights that can be stuck on the disc to make it tilt (weights do not translate on the disc) (see images attached). There is no friction whatsoever. The only force is gravitational...

I have a perfectly working 2-D finite-difference thermal solver, using an alternating-direction implicit scheme (painfully written in Fortran 90 at my adviser’s insistence), that I have recently extended to 3-D. It is essentially a three step approximation to the Crank-Nicolson equation, which...