What is Sphere: Definition and 1000 Discussions

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. brotherbobby

    The Indeterminacy of Problems with Multiple Friction Interfaces

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  2. S

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  3. Haorong Wu

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  4. colemc20

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  5. Haorong Wu

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  6. J

    MHB Integral Over Unit Sphere of Inner Product

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  7. peguerosdc

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  8. K

    Energy stored in a charged sphere

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  9. L

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  10. P

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  11. fight_club_alum

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  12. Kaguro

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  13. ?

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  14. J

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  15. hagopbul

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  16. L

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  17. arturo

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  18. PhysicS FAN

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  19. CharlieCW

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  20. L

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  21. Zack K

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  22. D

    Electronics Need a small motor and fan to blow air into a 4 inch sphere

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  23. C

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  24. C

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  25. K

    I Integrating discs to find the gravitational force of a sphere

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  26. T

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  27. A

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  28. AZFIREBALL

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  29. M

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  30. 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...
  31. Abdullah Wahid

    Positively Charged Metal Sphere: Reactivity & Capacitors

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  32. A

    Question regarding Ray Optics and Probability

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  33. 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...
  34. 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...
  35. C

    Path of a conducting sphere through a uniform magnetic field

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  36. Clara Chung

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  37. J

    Solid sphere rolling along a track

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  38. 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...
  39. Robin04

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  40. C

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    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. )
  41. H

    A Reference frame conversion for a moving sphere

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  42. Krushnaraj Pandya

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  43. B

    Optics Experiment involving transmission through a gel and a sphere

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  44. C

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  45. E

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  46. cookiemnstr510510

    Calculate the electric field in all of space for a non conducting sphere

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  47. N

    Potential of a non-conducting sphere

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  48. cookiemnstr510510

    Conducting Sphere With Cavity E-field / Gauss' law

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  49. cookiemnstr510510

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  50. isukatphysics69

    Determine the net charge of sphere C

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