Shape Definition and 613 Threads

this is not actually for homework, I am no longer in school, this is for a small application I am trying to write that compares dimensions. However, I believe this is the appropriate spot to post after reading the rules. Homework Statement okay, so let's say you got a shape, for example a...

Do you think it is possible to have a shape in the euclidean plane that has more than 2^{\aleph_0} sides. maybe some crazy fractal. and if not in the plane would we maybe have to go to infinite dimensional space.

I had read an article about a hot air balloon, when coming into balloon shape design, I had question on it. For best shape of the air balloon was the tear drop shape, but I do not know what is the physics behind it. From the article I read is about the pressure vector, and he is using an...

Homework Statement Does the size of the p orbital with the lone pair change when adding electron donating groups, such as methyl? Homework Equations N/A The Attempt at a Solution I know the electron availability increases on the nitrogen's lone pair, making it a better base, but I'm...

Hello, I would like to ask you some questions. 1) I've a closed curve (for example an ellipse, which may represent the contour of an object) represented by the set of its (known) points. I need to find the equation of that curve to pass through all and every point (exact fit). I think that...

Hi, This is my first post here. I think my question is relevant to the area of calculus hence posting here. In short: I suck at mathematics after years of trying, and I have a problem that I hope someone can help me with. Full disclosure: this is for a commercial project, so if that is not...

The event horizon of a Kerr black hole is often depicted as being spherical, but this seems to be a reference to the horizon as defined in Boyer-Lindquist coordinates, where horizons appear at a constant value of r. However, Thorne describes the "black hole's horizon bulg[ing] out at its...

Hi I have a problem where the flux of a particle beam is measured using a (nearly) perpendicular laser beam and a photomultiplier. I have a function looking like this: L(\nu) = \frac{\gamma/2}{(\nu - \nu_0 + kv)^2 +(\gamma^2/4)} I suppose this is a Lorentzian lineshape function...

Hi, I'm in the process of building a marble run out of brass wire using 15mm steel ball bearings. For ease of visualisation, it will be similar in principle to this: http://www.youtube.com/watch?v=0FRYX-kcZ9k&feature=relmfu I want to include a "jump" where the marble travels up a ramp at...

To give you a better idea, I have it drawn out here: http://tinypic.com/r/eq6ln5/6 I am calling the thickness of a rod t and the thickness of the shaft t2. I am using the basic equation Ixx = (integrate over area)(y^2)dA on different sections and then adding them all together, following the...

Hi all, I am trying to understand geometric flows, and in particular the Ricci flow. I understand how to calculate the metric tensor from the parametrization of a surface, but I am facing a problems in the concept phase. A metric tensor's purpose is to provide a coordinate invariant...

Homework Statement A block with a mass of 25 kg is hung midway between two pulleys, with a rope connecting a hook at the top of the block to each of the two pulleys. On the other side of the pulleys, both ropes are connected to blocks with masses of 15 kg. The 25 kg mass in the middle sags...

Homework Statement A block with a mass of 25 kg is hung midway between two pulleys, with a rope connecting a hook at the top of the block to each of the two pulleys. On the other side of the pulleys, both ropes are connected to blocks with masses of 15 kg. The 25 kg mass in the middle sags...

Hello: I would like to understand how to compute the shape operator (and eigenvalues etc) for a complex example like the Schwarzschild spacetime. It's easy for a submanifold in Euclidean space, but I don't know how to do it for the more advanced examples like the schwarzschild spacetime in...

A 180 degree circular arc (i.e. a half sphere) is obvious: When you rotate this about its two end points, you get a sphere. What about for something less than 180 degrees (e.g. 90)?: I believe this forms an ellipsoid, with coefficients a and b being equal, with respect to...

Hi: When a mass is accelerated, what happens to its length and volume? I know that when the acceleration ends, its length is governed by the equation l = l0 x sqrt (1 - v^2/C^2), but what about during the acceleration?

Hi Everyone, Imagine a tube of fabric stretched between two hoops, like the one's seen here.. http://www.stretchshapes.net/blog/wp-content/uploads/2012/08/A1.png That is, a cylinder made of an elastic material, under tension. Is there a name for this shape? Is there a generic equation...

In a game I'm developing, I have an ellipse which contains a blue shape inside of it like follows: http://img6.imageshack.us/img6/9518/screenshot20120815at938.png In the picture, the curves of the blue shape have the exact same arc as the area of the ellipse that it mirrors. In this...

How would you graph a square of any dimension on the cartesian coordinate system?

I had an idea of a planet that was spinning fast enough that at its equator, the outward force from the centripetal force would almost equate the planet's own gravity. However, this would change as you got closer and closer to the poles. I was just wondering what this planet might look like...

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"...

Hello. I read from a calculus book (Larson) that shape of comet's orbit is determined by its velocity in following way. Ellipse if v < sqrt(2GM/p) Parabola if v = sqrt(2GM/p) Hyperbola if v > sqrt(2GM/p) where p is the distance between one vertex and one focus of the comet's orbit...

If the universe began from the Big Bang, then why is the universe not a spherical shape? I mean, if it expanded from a singularity, then why is it not spherical?

Howde all. With reference to matter originating from the big bang. Nothing else. No multiverse, no pbranes - nothing. Just the Big Bang. Ok - given that galaxies are moving away from each other - then there is an overall outer edge shape created by these galaxies. Lets say now that...

for a 1D free particle with initial wave function \phi(x') square shaped(e.g. \phi(x')=1,x'\in [a,b],otherwise it vanishes), my question is: how does it evolve with time t? if we deal with it in P basis, it is easily solved, using the propagator U(t)=∫|p'><p'|e^{-\frac{ip'^2...

I am a bit confuse on the back EMF waveform shape of the brushless permanent magnet machine. As I know brushless DC permanent magnet motor has a trapezoidal shape back EMF waveform. If I use this motor as a generator, do I still get the same waveform shape or I will get a sinusoidal waveform?

this is from Krauss' A Universe from Nothing: I don't understand why that is the case. I don't need a real in depth explanation just a few nuggets of information.

Homework Statement Not homework, but something I'm interested in finding out. The setup is a flexible wire with left endpoint fixed at x=0 and right endpoint at x=L. You push the right endpoint with some horizontal force directed towards the left endpoint which will move the right endpoint...

[SIZE="4"]As we know a circle view at an angle appears as an ellipse , as you see in the picture, the center of the camera aim to the center of the circle , the angle between the circle axis and the camera is ө, the azimuth between mojor axis(a) and the camera is ∞, the rotation of the...

[SIZE="4"]As we know a circle view at an angle appears as an ellipse, as you see in the picture, the center of the camera aim to the center of the circle , the angle between the circle axis and the camera is ө, the azimuth between mojor axis(a) and the camera is ∞, the rotation of the...

Let's say we have 2 different conductors - one a round wire, another a round wire but with hollow core. The wire with the hollow core has higher resistance. But for the sake of argument, let's assume that it has the same resistance and the round wire. Will the skin effect be less for the...

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...

Sometimes I get frustrated with the dialogs in this forum because there are so many misunderstandings and outright half truths being passed around (including from myself). Well, I was just over at SciForums.com warily participating in the thread “According to SR…” and it gave me a whole new...

I am looking for an equation (or method to develop the equation) for bending of an irregular shape. I have only been able to find bending equations for beams. The attached picture shows the shape of the gusset being bent and the location of the force. If this were a beam it would be a cantilever...

Homework Statement I'm trying to determine the limits for a double integral over a symmetric trapezoid or equilateral triangle. I'm not trying to determine the area, and therefore using symmetry to simplify the integration is not an option. The limits for the integration over the y-axis are...

This isn't a homework question in its entirety, I'm just wondering what the difference is between a Mode ratio and a mode shape? I'm taking a mechanical vibrations course and trying to figure out what the problem is asking for when it wants a mode shape...

which would have greater pressure at the end, an L shape or Y shaped funnel?

What topic in mathematics would something fall under if you assumed a complex shape to be a more simple shape? Such as assuming a recliner is actually a cube, or a tree it actually a cone or prism, or a tire is actually a cylinder? Would this be topology, or something else? Simple geometry?

Homework Statement I need to find the bending moment of a washer shape for a project I'm working on so I don't have an exact problem statement. Imagine that a washer was fixed (not pinned) around its inner radius and a force were applied evenly around the outer radius. How can I go about...

Hello all, I've posted an image below of a very basic maths question I can't seem to solve. Even after looking at the correct answer I cannot seem to figure out how they got it no matter what I try. The question is: http://img684.imageshack.us/img684/6179/mr2q19.jpg From what I can...

Can intense harmonic vibrations cause an object to change shape to match the source or take that shape if it is plastic?

I'm wondering if there's a term for the property of spheres that makes gravity pull equally on all aspects of the sphere's mass. The wording for what I'm asking is tricky, so I'll give an example of a shape that wouldn't have this property, a long prism. If you drop a long prism on an angle...

For a container made of glass, what geometrical shape of the container would be best for maximum Total Internal Reflection, given that light incident on it is coming after reflection from a concave mirror? My hunch is that a cylindrical shape of the container is best, but I was not so sure...

EDIT: I meant to place this in Engineering help. Would a moderator please move it there? Thanks. Homework Statement I need to work out the theoretical principle second moment of area for an L shaped specimen I have...

This is from Spivak's Calculus. In an appendix, he defines polar coordinates. One of the exercises in this appendix is showing that the lemniscate, whose polar equation is: r^2=2(a^2)*cos(2theta) is the set of points P that satisfy that the product of the distances from said point to two...

I was wondering why, when I arrange six cylindrical magnets, about 1inch long and 1/5th inch wide each (neodymium magnets) in a hexagon shape by arranging them into a chain of N-S-N-S-N-S (top or bottom... with the other end obviously being opposite in arrangement) and connecting them into a...

Homework Statement When a paper cake case falls right way up through the air it quickly reaches terminal velocity. The drag force ,D, acting on the paper cupcake case is given by D=fpAv2(v is squared) Where p is the density of air which is 1.2 kgm-3 v is the terminal velocity A is the cross...

Is the VSEPR model a tool to help us visualize what is happening to molecules, or do the atoms really take on the shape of something like a trigonal bipyramidal?

Hey guys. I am trying to find a shape that suits my needs. The amount of vertexes can be any, but the fewer the better. The edges are special in that each end has an A or a B. like this A------B I need the vertexes to have more A than B inputs from edges. I need all vertexes to...

Basic chemistry: sulphur dioxide shape??! I realize this isn't homework, but it's so basic I'm ashamed of putting it in the chemistry section. I'm trying to self-teach here, but my textbook is awful and I'm even worse. Question: Workout the shape of SO2. Step 1: Draw lewis diagram to work out...