Sphere Definition and 1000 Threads

A sphere (from Greek σφαῖρα—sphaira, "globe, ball") is a geometrical object in three-dimensional space that is the surface of a ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space. This distance r is the radius of the ball, which is made up from all points with a distance less than (or, for a closed ball, less than or equal to) r from the given point, which is the center of the mathematical ball. These are also referred to as the radius and center of the sphere, respectively. The longest straight line segment through the ball, connecting two points of the sphere, passes through the center and its length is thus twice the radius; it is a diameter of both the sphere and its ball.
While outside mathematics the terms "sphere" and "ball" are sometimes used interchangeably, in mathematics the above distinction is made between a sphere, which is a two-dimensional closed surface embedded in a three-dimensional Euclidean space, and a ball, which is a three-dimensional shape that includes the sphere and everything inside the sphere (a closed ball), or, more often, just the points inside, but not on the sphere (an open ball). The distinction between ball and sphere has not always been maintained and especially older mathematical references talk about a sphere as a solid. This is analogous to the situation in the plane, where the terms "circle" and "disk" can also be confounded.

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  1. Lone Wolf

    What Is the Effect of Friction on the Height of a Sphere Rolling Down a Ramp?

    Figure: a) The mechanical energy of the sphere is conserved because the weight is the only force which does work. My problem with this question is mostly because the original picture (which I tried to recreate here) is kind of ambiguous, as in I don't know if H already accounts for the radius...
  2. J

    Understanding the physics behind an elastic sphere

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  3. JD_PM

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  4. J

    I Finding a linear combination to enter a sphere

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  5. migueldbg

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  6. brotherbobby

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  7. S

    Rotating Sphere: Conceptual Question

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  8. Haorong Wu

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  9. colemc20

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  10. Haorong Wu

    I How to understand the Bloch sphere in the quantum computation?

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  11. J

    MHB Integral Over Unit Sphere of Inner Product

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  12. peguerosdc

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  13. K

    What Potential Should Be Used for Energy Stored in a Charged Sphere?

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  14. L

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  15. P

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  16. fight_club_alum

    Volume charge density and potential difference in sphere

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  17. Kaguro

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  18. ?

    Rotating sphere which separates into hemispheres

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  19. J

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  20. hagopbul

    I Absorption of Radiation: Calculating Sphere Area

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  21. L

    I Finding the coordinates of a point on a sphere

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  22. arturo

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  23. PhysicS FAN

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  24. CharlieCW

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  25. L

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  26. Zack K

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  27. D

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  28. C

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  29. C

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  30. K

    I Integrating discs to find the gravitational force of a sphere

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  31. T

    A ball (sphere) rotating along a moving incline

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  32. A

    Variable induced surface charge density on a sphere

    Homework Statement Homework Equations While solving this problem at r >>a ,the corresponding potential due to the dipole is kpcosθ/r2(potential due a dipole) where k is the electrostatic constt. ...(1) If σ(θ) is the surface charge density induced due to external electric field. then the...
  33. AZFIREBALL

    B What would it be like on Earth if it were not a sphere?

    Since I was very young I have wondered what life would be like if the Earth was a different shape. For example, what if Earth were two spheres stuck together rather than just a single sphere?Say the Earth consisted of two, same size, spheres connected at what is now our north pole with a...
  34. M

    Surface area of a shifted sphere in spherical coordinates

    Homework Statement find the surface area of a sphere shifted R in the z direction using spherical coordinate system. Homework Equations $$S= \int\int \rho^2 sin(\theta) d\theta d\phi$$ $$x^2+y^2+(z-R)^2=R^2$$ The Attempt at a Solution I tried to use the sphere equation mentioned above and...
  35. jk22

    B Dimension of the metric of a projection of a sphere

    Let ##(x_1,x_2,x_3)=\vec{r}(\theta,\phi)## the parametrization of a usual sphere. If we consider a projection in two dimension ##(a,b)=\vec{f}(x_1,x_2,x_3)## Then I don't understand how to use the metric, since it is ##g_{ij}=\langle \frac{\partial\vec{f}}{\partial...
  36. Abdullah Wahid

    Positively Charged Metal Sphere: Reactivity & Capacitors

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  37. A

    Question regarding Ray Optics and Probability

    Let there be a sphere whose inner surface consists of a perfectly reflecting surface. It has a hole on it which allows a ray of light to enter. Give the angle made with the normal of the hole when the ray of light enters such that the probability that the ray comes out is the least?Assuming the...
  38. Clara Chung

    Question about a conducting sphere in a varying magnetic field

    Homework Statement 3. A spherical conducting shell is placed in a time-varying magnetic field. Is there an induced current along the equator? Homework EquationsThe Attempt at a Solution I don't know what is the right answer. I mean...why not? Is the magnetic field is changing, there should be...
  39. T

    Electric field of a non-conducting sphere

    Homework Statement A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r1= R/4 the electric field has a magnitude Eo. What is the magnitude of the electric field at a radial distance r2=2R? Homework Equations Gauss's Law: ∫EdA=Qencl / ε0 Charge...
  40. C

    Path of a conducting sphere through a uniform magnetic field

    Hello, could someone help answer this question for me: How would the path of a conducting sphere (i.e. AL) be affected as it passes through a strong uniform magnetic field orthogonal to the direction of motion. I believe the Lenz effect/Eddy currents will create a magnetic field opposing the...
  41. Clara Chung

    Metal sphere in an electric field

    Homework Statement The question is exactly the same as this question https://physics.stackexchange.com/questions/250297/metal-sphere-in-a-uniform-electric-field However, it says "Then by symmetry the entire xy plane is at potential zero" in the book. I don't understand this. Homework...
  42. J

    Solid sphere rolling along a track

    Homework Statement Please see the attached file. Homework Equations Ei = Ef The Attempt at a Solution I don't have an answer key provided, but I'd really like to verify that I'm right (or if I'm wrong, why). I think ti'd be (c) because assuming that due to inertia, B will continue going...
  43. X

    I How Do You Transform Qubit States Between Different Bases on the Bloch Sphere?

    Anyone know how to change a basis of a qubit state of bloch sphere given a general qubit state? There are 3 different basis corresponding to each direction x,y,z where |1> ,|0> is the z basis, |+>, |-> is the x basis and another 2 ket notation for y basis. Given a single state in the x basis...
  44. Robin04

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  45. C

    Is there any tensor that gives the radius of a sphere?

    Can I calculate a tensor of a system( lots of particles) shaped like a sphere, then get exactly the radius of the system? (I want to get lengths of three axes of ellipsoid, and I'm trying to examine the way with a sphere. )
  46. H

    A Reference frame conversion for a moving sphere

    Hi here is the situation; There's a spherical particle contained with a MEMS sensor (3D accelerometer and gyroscope) moving down a bed. What we want is to estimate the total kinetic energy of the particle. The total kinetic energy has two parts, translational part and rotational part. for the...
  47. Krushnaraj Pandya

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  48. B

    Optics Experiment involving transmission through a gel and a sphere

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  49. C

    Finding the energy density outside of an isolated charged sphere

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  50. E

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