volume of a 10D hypersphere

does anyone know the volume of a ten dimensional unit hypersphere? my mate is trying to work it out for a omputing project but he keeps on getting silly answers

Reply 1

elpaw

oops sorry wrong forum, i was going to post this in the academic section

Reply 2

You know, I just happen to have this figure, let me see my notes...its 2.5502.

Reply 3

elpaw

2776

You know, I just happen to have this figure, let me see my notes...its 2.5502.

yeah, that's the sort of answers he's been getting. cheers for that.

Reply 4

username9816

elpaw

volume of a ten dimensional unit hypersphere?

whats that? :confused:

Reply 5

elpaw

bono

whats that? :confused:

the volume of the following equality: x² + y² + z² + t² + a² + b² + c² + d² + e² + f² <= 1

Reply 6

Have a look at this if you are interested:

http://www.mathreference.com/ca-int,hsp.html

Reply 7

Jonatan

elpaw

does anyone know the volume of a ten dimensional unit hypersphere? my mate is trying to work it out for a omputing project but he keeps on getting silly answers

Are we talking about the 10D hypervolume or the 3D volume on the 3D "surface" of a 10D hypersphere?

Reply 8

elpaw

Jonatan

Are we talking about the 10D hypervolume or the 3D volume on the 3D "surface" of a 10D hypersphere?

the actual hypervolume. its meant to be some fraction of pi, but i cant find this fraction anywhere.

Reply 9

username9816

elpaw

the actual hypervolume. its meant to be some fraction of pi, but i cant find this fraction anywhere.

But I thought 2776 helped you?

Reply 10

elpaw

bono

But I thought 2776 helped you?

he did but he gave the decimal approximation.

Reply 11

username9816

elpaw

he did but he gave the decimal approximation.

whats wrong with that?

Reply 12

elpaw

he did but he gave the decimal approximation.

Try:

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

http://matcmadison.edu/alehnen/sphere/hypers.htm

Reply 13

Nylex

bono

whats wrong with that?

Decimals aren't exact, whereas fractions are..

Reply 14

Nylex

Decimals aren't exact, whereas fractions are..

However the decimal approx. Would have given him an indication of whether the answer he got was correct or not.

Reply 15

username9816

Nylex

Decimals aren't exact, whereas fractions are..

well obviously, but i don't understand why a decimal value isn't sufficient in his case.

Reply 16

username9816

2776

However the decimal approx. Would have given him an indication of whether the answer he got was correct or not.

Exactly, that was my point, i thought the decimal answer would have been of more use.

Reply 17

elpaw

2776

However the decimal approx. Would have given him an indication of whether the answer he got was correct or not.

thanks for the help. im not getting the answer, my friend is. it's his computing project, not mine (mine's on radioactivity).

Reply 18

username9816

elpaw

thanks for the help. im not getting the answer, my friend is. it's his computing project, not mine (mine's on radioactivity).

just wanted to ask elpaw, when u say computing project, how do u mean exactly?

just curious as to what the project is about. :smile:

Reply 19

Jonatan

elpaw

does anyone know the volume of a ten dimensional unit hypersphere? my mate is trying to work it out for a omputing project but he keeps on getting silly answers

Sounds like an integration problem. My advice is to start with a one dimensional circle (two points) and then rotate that circle in another dimension to get a circle of the next dimension (thus if you rotate a 1D cricle you get a 2D circle. Rotate this circle you get a sphere, rotate the sphere you get a hypersphere etc etc )

The nD volume of each nD sphere you find using volumes of rotation. Think this should work.