- #1

yourdadonapogostick

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- Thread starter yourdadonapogostick
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- #1

yourdadonapogostick

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- #2

Gokul43201

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No, the n-sphere is the surface defined by the equality.

- #3

yourdadonapogostick

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who what is the inequality?

- #4

Gokul43201

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http://mathworld.wolfram.com/Hypersphere.html

- #5

Gokul43201

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- #6

yourdadonapogostick

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i know that, i was asking what the points inside(the inequality) is called, since it isn't a sphere.

- #7

Gokul43201

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I guess you'd simply call them "points inside the n-sphere" (?), though I'm not sure if 'inside' is well defined. In this case, though, you could define 'inside' as being on the same side of the surface as the center.

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- #8

yourdadonapogostick

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the volume which said n-sphere encapsulates?

- #9

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How about "interior of the (n+1)-ball"?

- #10

[tex]\sum_{i=1}^{n} (x_i-c_i)^2{\leq}r^2[/tex]

is a closed n-ball or radius

[tex]\sum_{i=1}^{n} (x_i-c_i)^2< r^2[/tex]

is an open n-ball or radius r or "open ball" in R^n.

Note that in R^n, a ball is n-dimensional and a sphere is (n-1)-dimensional; i.e., a topologist's n-sphere is the boundary of an (n+1)-ball.

- #11

matt grime

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The interiot is commonly called a ball or a disc.

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