In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere. It may be a closed ball (including the boundary points that constitute the sphere) or an open ball (excluding them). In Euclidean space, a ball is the volume bounded by a sphere These concepts are defined not only in three-dimensional Euclidean space but also for lower and higher dimensions, and for metric spaces in general. A ball in n dimensions is called a hyperball or n-ball and is bounded by a hypersphere or (n−1)-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. In a one-dimensional space, a ball is a line segment. In other contexts, such as in Euclidean geometry and informal use, sphere is sometimes used to mean ball. In Euclidean n-space, an (open) n-ball of radius r and center x is the set of all points of distance less than r from x. A closed n-ball of radius r is the set of all points of distance less than or equal to r away from x. In Euclidean n-space, every ball is bounded by a hypersphere. The ball is a bounded interval when n = 1, is a disk bounded by a circle when n = 2, and is bounded by a sphere when n = 3. One may talk about balls in any topological space X, not necessarily induced by a metric. An (open or closed) n-dimensional topological ball of X is any subset of X which is homeomorphic to an (open or closed) Euclidean n-ball. Topological n-balls are important in combinatorial topology, as the building blocks of cell complexes. Any open topological n-ball is homeomorphic to the Cartesian space Rn and to the open unit n-cube (hypercube) (0, 1)n ⊆ Rn. Any closed topological n-ball is homeomorphic to the closed n-cube [0, 1]n. An n-ball is homeomorphic to an m-ball if and only if n = m. The homeomorphisms between an open n-ball B and Rn can be classified in two classes, that can be identified with the two possible topological orientations of B. A topological n-ball need not be smooth; if it is smooth, it need not be diffeomorphic to a Euclidean n-ball.
I THOUGHT I WAS THE ONLY THAT RECOGNIZED THE SIMILARITIES!!!!
Thx for curing my insanity.
they aren't like the same songs but in different versions? it's very similar
"Dota", "Rave Girl" and "All I ever wanted"
This is the most 2008 video I have ever seen
thank you :-)
Track of every scene girl in MySpace lol
omg these songs r both gr8 on their own, but dis is amazinggg ily
i only just realised how similar these songs were because someone was humming one of these and i couldnt tell which
DUDE I WAS LOOKING FOR THISSS
I was searching for this one thank you!!!
я ждал этой склейки...)
why was this on my recommended-
i'm not complaining tho
Daddy DJ on Tha Spinnin Toilet
real.
I KNOW THIS PRETTYRAVE GIRL
first
this is fantastic
you are the MA N
Bangers
My brain at 3 a.m.
fuck yeah
hi
3rd!!!¡!!
Sound the same lol
good lord this is atrocious
hell yeah
youre not even a doctor
In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere. It may be a closed ball (including the boundary points that constitute the sphere) or an open ball (excluding them).
In Euclidean space, a ball is the volume bounded by a sphere
These concepts are defined not only in three-dimensional Euclidean space but also for lower and higher dimensions, and for metric spaces in general. A ball in n dimensions is called a hyperball or n-ball and is bounded by a hypersphere or (n−1)-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. In a one-dimensional space, a ball is a line segment.
In other contexts, such as in Euclidean geometry and informal use, sphere is sometimes used to mean ball.
In Euclidean n-space, an (open) n-ball of radius r and center x is the set of all points of distance less than r from x. A closed n-ball of radius r is the set of all points of distance less than or equal to r away from x.
In Euclidean n-space, every ball is bounded by a hypersphere. The ball is a bounded interval when n = 1, is a disk bounded by a circle when n = 2, and is bounded by a sphere when n = 3.
One may talk about balls in any topological space X, not necessarily induced by a metric. An (open or closed) n-dimensional topological ball of X is any subset of X which is homeomorphic to an (open or closed) Euclidean n-ball. Topological n-balls are important in combinatorial topology, as the building blocks of cell complexes.
Any open topological n-ball is homeomorphic to the Cartesian space Rn and to the open unit n-cube (hypercube) (0, 1)n ⊆ Rn. Any closed topological n-ball is homeomorphic to the closed n-cube [0, 1]n.
An n-ball is homeomorphic to an m-ball if and only if n = m. The homeomorphisms between an open n-ball B and Rn can be classified in two classes, that can be identified with the two possible topological orientations of B.
A topological n-ball need not be smooth; if it is smooth, it need not be diffeomorphic to a Euclidean n-ball.
@@C1RCU1TBOARD THANK YOU. FINALLY someone says it SHEESH❗