What is Shape: Definition and 635 Discussions

A shape or figure is the form of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type.
A plane shape, two-dimensional shape, or 2D shape (plane figure, two-dimensional figure, or 2D figure) is constrained to lie on a plane, in contrast to solid figures.

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  1. S

    Finding the shape of a function

    While I was doing exercises about this, I noticed that, for example f(x,y)=e^{x^2+y^2} was very similar to f(x,y)=x^2+y^2 And something similar with: f(x,y)=e^{(1-x^2-y^2)^{(1/2)}} and f(x,y)=(1-x^2-y^2)^{(1/2)} So I supposed that some transformations that preserves some properties kinda...
  2. C

    Shape of Universe: Is Flatness Approved? Causes of Big Crunch

    How certainly is the universe flat? Is is absolutely approved or not? If yes, what will cause the big crunch?
  3. Gh778

    Efficiency to move a curve shape

    Fig 1 : the blue volume has a lot of very small spherical balls in it. Balls are under pressure from external system (weight or other), the potential energy is always the same because the blue volume is constant. When I move the blue volume from position 1 to position 2, I can understand that...
  4. A

    Looking for a good analogy of the shape of the expanding universe

    I have heard people say there is no center to the expansion of the universe. I have also heard the expansion described as an ever expanding balloon with all galaxies as dots on the surface. These to statements seem contradictorily to me. If the expansion of the universe was like the above...
  5. M

    Does a Conical End Affect the Magnetic Field Strength of a Solenoid?

    If instead of a disc shaped end I have a conical end , would there be any change in the measured magnetic field strength at the end of the solenoid keeping current, core and number of turns per unit length constant ?
  6. Gh778

    Can the Difference in Pressure Create a Zero Torque in a Curved System?

    Hi, I'm interesting about the torque in the system like I drawn. I drawn only additional forces from curve, not the true forces from absolute pressure. The shape is full with a lot of very small circular balls (blue color). A pressure is apply from external system. The goal is to have FR...
  7. X

    Difference in shape, LxWxH, most similar proportions, regardless of scale

    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...
  8. C

    Is There a Shape with More than 2^{\aleph_0} Sides in the Euclidean Plane?

    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.
  9. P

    Why Is the Tear Drop Shape Optimal for Hot Air Balloons?

    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...
  10. C

    Do Amine Orbitals Change Shape

    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...
  11. G

    Deriving the equation of points for exact fitting and shape analysis

    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...
  12. M

    Find the line that gives constant area in odd shape

    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...
  13. G

    Shape of Kerr event horizon in terms of reduced circumference

    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...
  14. C

    Lorentzian line shape function

    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...
  15. J

    What shape ramp for maximum marble jump?

    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...
  16. M

    Calculating the Moment of Inertia of an Irregular Rod Shape

    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...
  17. M

    How does changing the metric on a manifold affect the shape of the manifold?

    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...
  18. L

    3 weights suspended on 2 pulleys to form a M shape

    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...
  19. L

    Three blocks suspended on 2 pulleys to form a M shape

    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...
  20. H

    Shape Operator for Schwarzschild spacetime in 2-dim

    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...
  21. D

    Judging distribution shape using mean and standard deviation

    Homework Statement A recent summary for the distribution of cigarette taxes (in cents) among the 50 states and Washington, D.C. in the United States reported mean = 73 and standard deviation = 48. Based on these values, do you think that this distribution us bell-shaped? Justify your answer...
  22. M

    What Does Rotating a Circular Arc Create?

    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...
  23. B

    What happens to the shape of an accelerating mass

    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?
  24. S

    Stretched fabric cylinder between two hoops - what is the shape?

    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...
  25. M

    Positioning Shape Inside of Ellipse

    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...
  26. mesa

    Question about graphing a shape on the cartesian coordinate system

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

    Lorentzian line shape profile

    Hi I hope some one can help me with this one: I have a Lorentzian line profile L(√L) = 1 / ((√L - √0 )^2 + (\Gamma2/4)) for v = 0. For v \neq 0 I have \int(1 / ((√L - √0 - kvz)^2 + (\Gamma2/4)) * g(vz) dvz) I suppose the factor g(vz) dvz is a velocity factor, but how do I...
  28. T

    Shape of a planet spinning very quikly

    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...
  29. B

    Maximum volume of a 3D shape with 3 identical circular profiles from x,y,z.

    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"...
  30. 4

    What is the relationship between a comet's velocity and the shape of its orbit?

    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...
  31. T

    Shape of Universe: Why Is It Not Spherical?

    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?
  32. A

    Discovering the Shape of Spacetime from the Big Bang: A Scientific Exploration

    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...
  33. Y

    Square shape wave packet spreading

    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...
  34. V

    The difference of Back EMF waveform shape of BLDC and brushless PM generator

    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?
  35. R

    How the shape of the universe affects density

    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.
  36. S

    What shape will a bent wire take?

    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...
  37. T

    Trying to improve heat flow through a rod by changing its shape.

    Hi all, I have a mostly theoretical question here. I have a copper rod approximately 2cm in diameter and 3cm tall. It is fit snugly inside a much taller cylinder. Heat enters through the base of the copper rod and exits through the sides into the tall cylinder. I need to improve conduction...
  38. O

    How to predict the shape of the circle from any point of view

    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 camera is €...
  39. O

    How to predict the shape of the circle from any point of view?

    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 camera is €...
  40. L

    Skin Effect and shape of conductor

    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...
  41. K

    What's it called when a 3D shape can be made of 2D surfaces of all the same size

    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...
  42. M

    Effect of acceleration on shape and size of a light wave front

    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...
  43. D

    Design Considerations for Bending of Irregular Shaped Brackets

    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...
  44. D

    Limits for double integral over trapezoidal shape

    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...
  45. M

    What is the difference between mode ratio and mode shape?

    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...
  46. B

    Which would have greater pressure at the end, an L shape or Y shaped

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

    Assuming Complex Shape a Simple Shape. What is this called?

    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?
  48. E

    Bending moment and stress of a washer shape

    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...
  49. C

    Basic Math - How to find the area of this composite shape?

    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...
  50. J

    Does Shape Determine Frequency?

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