Register to reply

S^5 sphere

by yola
Tags: sphere
Share this thread:
yola
#1
Feb1-11, 02:44 AM
P: 17
What does S^5 sphere mean? How can I imagine it?
Thanks
Phys.Org News Partner Mathematics news on Phys.org
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
torquil
#2
Feb1-11, 03:32 AM
P: 641
http://en.wikipedia.org/wiki/Hypersphere
HallsofIvy
#3
Feb1-11, 05:15 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,293
It is the subset of R5 of points [itex](x_1, x_2, x_3, x_4, x_5)[/itex] such that
[tex]x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2= 1[/tex]

(The "Ball", B5, is the set of points [itex](x_1, x_2, x_3, x_4, x_5)[/itex] such that
[tex]x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2<= 1[/tex])

torquil
#4
Feb1-11, 05:31 PM
P: 641
S^5 sphere

Quote Quote by HallsofIvy View Post
It is the subset of R5 of points [itex](x_1, x_2, x_3, x_4, x_5)[/itex] such that
[tex]x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2= 1[/tex]

(The "Ball", B5, is the set of points [itex](x_1, x_2, x_3, x_4, x_5)[/itex] such that
[tex]x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2<= 1[/tex])
No, S^5 is the unit sphere in R^6, not of R^5. It should be five-dimensional, not four-dimensional. Your B^5 is correct, though.
mathwonk
#5
Feb1-11, 06:08 PM
Sci Advisor
HW Helper
mathwonk's Avatar
P: 9,453
you might try computing the volume of B^5 to get a first idea of what it "looks" like. and then maybe you can deduce the "area" of S^4.


Register to reply

Related Discussions
Solid sphere inside a hollow sphere. Introductory Physics Homework 14
Finding corrections to volume of a two-sphere in 3-sphere geometry Calculus & Beyond Homework 1
Resistance for a sphere in a half sphere containing liquid Introductory Physics Homework 19
Moving a coordinate system around a sphere where z axis pointing to sphere origin. Engineering, Comp Sci, & Technology Homework 1
Rotate point on sphere to exactly 'cut sphere in half' Differential Geometry 11