1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Surface area of a Hypersphere?

  1. Aug 5, 2014 #1
    I'm wondering how to scale up the surface area of a sphere of 6 million meters in radius, into a hypersphere of similar radius (i.e. a Hyper Earth). I would also like to know the ratio.

    I would like to know the basic value in 4th dimension, but knowing values for 5th, 6th, and higher would be useful too. I attempted using something like pi^2*r^3 after badly integrating numbers that probably shouldn't be integrated, but then I got confused, because the units produced different surface areas. like if the unit is 1 earth radius, then taking it to the 3rd, 4th, or 5th power doesn't change the output, and if the units are km, they produce a smaller change than if the units are meters, or nanometers. I got so lost on this issue that I decided to post here.
  2. jcsd
  3. Aug 5, 2014 #2


    Staff: Mentor

  4. Aug 6, 2014 #3
    Wikipedia articles are Gibberish, not informative. from what I got out of that they imagined Pi from thin air and then applied it to S_n(R) = S_n R^n and n-sphere in (n + 1)-dimensional Euclidean... which from what I am reading says n = 4 since thats my happy dimension to start with, and 4+1 = 5.

    now I stick 5 in the n place, and get
    Surface area of a 6e6m radius sphere is 6e6^5, which is about 68 on a decibel scale, times 5, which is about 340, or 1e34 times s sub 4 which for some unknown reason in 3 dimensions becomes 4 so uhh.. 8pi*1e34?

    Now you know that's not the answer.

    So how about a more sincere reply to my question than "go to wikipedia" ?
  5. Aug 6, 2014 #4


    User Avatar
    Homework Helper

    It's gibberish if you don't understand it.

    In reality, the Earth is a 3-ball (volume is 3 dimensional) and a 2-sphere (surface area is 2 dimensional).

    Now this is gibberish!
  6. Aug 7, 2014 #5


    User Avatar
    Science Advisor
    Homework Helper

    I think the surface area is always the derivative (wrt R) of the volume, and the volume of a 4-ball is π^2R^4/2, I believe. so the surface area of a 4 sphere is lets see: 2π^2R^3?? see my notes for the epsilon geometry camp for bright 9 year olds, last pages.

    http://www.math.uga.edu/~roy/camp2011/10.pdf [Broken]
    Last edited by a moderator: May 6, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook