Geometrical Definition and 144 Threads

Hello all, I am curious to know if any of you have ever used the Monte Carlo method to solve problems involving thermal radiation exchange. An overview of the problems that can be solved using this method is described here...

Is it possible for me to use a Voronoi diagram - or some other algorithm - to represent a point in an multidimensional space (between 5 and 10 dimensions) in a 2D geometrical shape? (And more interestingly, in a geometrical shape that is a) fairly small, and b) looks aesthetic. I have a...

So I’m trying to visualize what is going on in QM geometrically. More specifically I would like to visualize the time dependent wave equation in 3 dimensions. So let’s start with dimensionality. Normally when I think of a function of some variables, I picture it in a space with the number of...

The notion of spectrum in algebraic geometry seem to be a bit abstract to me. Is it a set of points? Is it the analogue of spectrum in Fourier transform?

Hi! I am trying to find out where: cos\theta=\frac{a \cdot b}{|a||b|} came from. Here is mine geometrical interpretation of scalar projection: Now, (pr means projection) pr_{\overrightarrow{A}} \overrightarrow{B} = p\overrightarrow{B_0} and...

Geometry is arguably my weakest link in mathematics. The answers just don't "hit me" in geometry like some other sections of math do. When trying to prove something in a polygon, such as congruence of triangles made by segments etc. I find it difficult since the equal sides/angles aren't...

Hello again, another vector question. The diagram (not included) shows a parallelogram OABC with OA=a and OC=c; AC and OB intersect at point D such that OD=hOB and AD=kAC. How do I show what h and k equal? I managed to achieve: a+c=2DB+AD-DC=2OD+DC-AD=OB and c-a=2DC+OD-DB=2AD+DB-OD=AC...

Lets imagine following: We have an infinite set of numbers representing the time. Now if we want to know how much time has spent in a specific sequence of this infinite set we see that this is impossible because there is infinite time passed before this sequence and infinite time passed...

Homework Statement A needle of length 5.0cm placed at the bottom of a beaker and a converging lens of focal length 20.0cm is held 30.0cm from the needle.The needle is illuminated with a lamp from the bottom.An image of the needle is formed on a screen.The beaker is now filled with...

I had to draw these diagrams for an AP Physics summer work assignment. I was just wondering if someone could look them over and let me know if I did them correctly. Thanks! http://img356.imageshack.us/img356/5520/go1kf2.png" http://img354.imageshack.us/img354/8011/go2lj2.png"

Homework Statement A lens is made of glass for which the refractive index is n[r]=1.5 for red beams and n[v]=1.52 for violet beams. radii of both surfaces are the same and equal R=1m. Find the distance between foci for red and violet beams Homework Equations The Attempt at a Solution

i really can not understand it

Hello, In a geometrical algebra exercise I have to solve the equation k F = 0, where k is a vector and F is a bivector (plane). From this it follows that also \mathbf{k} \wedge F = 0, which basically says that the vector k is perpendicular to the plane F. We are supposed to show (among other...

What is geometrical shadow qualitatively? please don't refer me to hyper physics

Prove that the graph of y= ax^3 + bx^2 + cx + d has two distinct turning points if b^2> 3ac. Find values of a,b,c and d for which the graph of this form has turning points at (0.5, 1) and (1.5, -1)

Would a geometrical structure following a single set of simple rules when it tessellates that: 1) Predicts the mass ratio of the electron to the proton 2) Derives and explains the fine structure constant 3) Explains the reason for only 3 generations of matter 4) Predicts the electron...

Does anyone know what the geometrical interpretation of a dot product in 3-D is? I am calculating the dot product between two vectors in 3d and need to use the |a||b|cos(theta) interpretation basically, but that is for 2d. Can I just tack on an additional cos(theta2)? Thanks a lot for your...

http://img140.imageshack.us/my.php?image=jonesf2238vg1.gif Problem Statement: Two prisms with the same angle but different indices of refraction are put together to form a parallel sided block of glass (see the figure). The index of the first prism is n1 = 1.48 and that of the second prism is...

do you hate it to? note this is not an anonymous ballet in case someone votes the second option so that i can berate them.

I've stumbled upon what might be a geometrical interpretation of Taylor's series for sine and cosine. Instead of deriving the Taylor's series by summing infinite derivatives over factorials, I can derive the same approximation from purely geometrical constructs. I'm wondering if something...

how can i solve this problem!?? thx

Homework Statement An object is located 2 m away from a convex mirror with radius of curvature of 1 m. (a) Draw the ray trace diagram (observe scale!) and use that to deduce where the image occurs (b) What is the distance between the image and the mirror? (c) Strike out that which is...

Homework Statement Explain why for a given object screen distance there are two positions where the image is in focus. Is this always true? Homework Equations The Attempt at a Solution

Let f and g be real differentiable functions. Let v be a vectorial function of a real variable t, such that: v(t) = ( f(t), g(t) ) I know that by definition v'(t) = ( f'(t), g'(t) ) In many books they give a geomtrical interpretation of this. They draw the curve (the values of f(t) in...

I am looking for some good websites that have proofs involving parallelograms and rhombus'? preferably in statement and reasons format any help would be appreciated. thank you

I'm reading Schutz's text Geometrical methods of mathematical physics right now as a part of a diredcted study (Two of my former math professors and I wish to learn the subject together so we formed a group for self-study). I know the material in a general sense but not at the precision of this...

The first derivative represents the slope of a tangent at a point on the function's curve. The second derivative represents the concavity of the function's curve. However I am unable to figure out what the other derivatives of a function represent either physically or geometrically. Pleae help.

A convex lens of focal length f is placed in front of a convex mirror having the same principal axis as the lens. Construct the path of a ray of light which coincides with the corresponding ray emerging from the lens-mirror system, and the path of the ray whose corresponding emergent ray is its...

If one can draw (or represent) a 3 dimensional figure on a 2 dimensional surface (ie-a cube on a blackboard), is it possible to "draw" (or represent) a 4 dimensional "figure" on a 3 dimensional "surface"?

I'm having some trouble with a couple of Optics questions, any hints would be much appreciated! THe first quetion states that a concave mirror forms an image on a screen twice as large as the object. The object and the screen are then moved such that the new image produced is 3x's the size...

I have my question,doubt and solution in the attachment that followed.Thanks for anybody that spend some time on this question.Sorry to say that the file format is *.zip .

I have my question,doubt and solution in the attachment that followed.Thanks for anybody that spend some time on this question.Sorry to say that the file format is *.zip .

Dear Friends I'd like to know if anybody has the solution of the aplication of nabla's operator to geometrical product: ab=a·b+a^b And if it's possible to apply a operator like this: d/dt + d/dx i + d/dy j + d/dz k. My best reggards.

Hey guys and gals...i am really stuff on dis question.. n i really need 2 knw homework 2 do dis.. so ne1 please help..n post der views...cheers! Design a converging achromatic lens of focal length 100cm. Refractive indices and dispersive powers for the two glasses available are 1.51 and 0.016...

Geometrical optics help?? Design a converging achromatic lens of focal length 100cm. Refractive indices and dispersive powers for the two glasses available are 1.51 and 0.016 for crown glass and 1.61 and 0.026 for flint glass. The converging element of the achromat is to be bi-convex and the...

Hi Could someone point me to websites with tutorials on the real-virtual sign convention for geometric optics (and possibly other known conventions too)? I've been googling for some time but the results aren't too satisfying. PS--Tutorials with mathematics are preferred... Thanks and...

I am not completely satisfied with Griffith's explanation for the geometrical interpretation of a gradient. Can someone elaborate on the geometrical meaning of the magnitude and the direction of a gradient?

Kindly explain the significance of the geometrical moment of inertia. i=\int y^2dA y is the distance from the axis, dA is the area element spacetime www.geocities.com/physics_all/

Would anyone happen to know any free software available for download, which could allow me to quickly draft circles, quads, and label vertices, radii, etc. ? I have several other programs, but they simply take too much time. Thank you again.

Hi all, i am interested in finding out the Geometrical properties of an arbitrary section, which means 2D area. Rather than having to perform manual calculations everytime, i am trying to write a program to help me with this. There is a problem however. I cannot seem to find the appropriate...

I just have a few questions on geometrical optics. 1. Why do the hands of a clock move counterclockwise in a mirror? 2. If you move farther away from a plane mirror, will you be able to see more of yourself or less? 3. How do you decide if the image in a mirror is real or virtual...

New Geometrical Polar-Ring Solution for Magic Numbered Nuclei. It is well known that if the neutron- or proton number within atomic nuclei have the following quantities (2, 8, 20, 28, 50, 82 and 126: the magic numbers), then the atoms are showing a more than average stability. As an example...

In the previous theme I spoke, that tangential energy of the dipole of speed is proportional to its square. Accordingly, tangential energy of radial resonance oscillations of the energy ring is proportional to the total square of all dipoles of speed in the ring. See file "dipole of speed.pdf"...

Could we give a geometrical meaning of the Lorentz equation mx´´=e(vxB)+eE...similar to that of gravitation..by considering that e(vxB)+eE comes from a potential..and the electrons are moving in geodesics?..