1. Not finding help here? Sign up for a free 30min 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!

What is a Hypersurface?

  1. Jan 31, 2004 #1
    I'm new to the physics scene. I'm trying to get into it. I just read my first book the other day in fact. In the book it mentioned hypersurface. I've also heard it referred to as hyperplane. Hypersurface intrigued me a lot and I wanted to learn more about it. I did some research on the internet. The one thing I wanted to find I couldn't find... the formula. Does anyone know the hypersurface formula? Know where I can get it? Any help will be greatly appreciated.
     
  2. jcsd
  3. Jan 31, 2004 #2
    You'd do best to start your research with a search for "Flatland: A Romance of Many Dimensions." It's a copyright-expired work, so you'll find many copies of it available free of charge on the 'net. To be honest, I've never read the original work, which I understand is as concerned with political and social satire as it is with mathematical rigour; I've read many works that cite it and expand on its principles.

    The basic idea is this: to understand something in four dimensions, imagine yourself explaining the 3D version to a 2D person. Want to know what a 'hypercube' is like? Imagine explaining 'cube' to someone who has only seen squares.

    We use 'hyper' to refer to anything that exists in more than three dimensions, but often to four dimensions. A table of terminology:

    2D 3D 4D
    line plane hyperplane
    circle sphere hypersphere (or 'glome')
    curve surface hypersurface

    You can develop the functions for hyperplanes and glomes by analogy:

    line: ax + by = c
    plane: ax + by + cz = d
    hyperplane: ax + by + cz + dw = e

    circle: x^2 + y^2 = r^2
    sphere: x^2 + y^2 + z^2 = r^2
    glome: x^2 + y^2 + z^2 + w^2 = r^2

    The glome and the hyperplane are two examples of hypersurfaces. Just as you can create a three-dimensional surface by rotating, dragging, or otherwise mistreating a two-dimensional curve (like a parabola, circle, line, exponential curve...), there are any number of four-dimensional hypersurfaces that you can create by starting with three-dimensional surfaces.

    P
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: What is a Hypersurface?
  1. What if ? (Replies: 31)

  2. What if (Replies: 2)

  3. What is . (Replies: 3)

  4. What is this (Replies: 2)

  5. What is this? (Replies: 6)

Loading...