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!

Is there any pyramid like that?

  1. Oct 9, 2015 #1
    I had geometry quite a while ago and I wonder if anyone has any idea how to tackle this problem:

    Is there any ABCDS pyramid (where ABCD is a rectangle) in which each 2 edges have different lengths and |AS|+|CS|=|BS|+|DS|

  2. jcsd
  3. Oct 9, 2015 #2


    Staff: Mentor

    Welcome to PF!

    Do you mean a real pyramid like the ones in Egypt or mathematically?
  4. Oct 9, 2015 #3
    :smile: mathematically. Something tells me one can construct such a pyramid, but I cant give explicit example..
  5. Oct 9, 2015 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No Egyptian pyramids I know of have a rectangular floor plan....

    I assume the unequal edges are only the non-horizontal ones (because of this rectangular floor plan) ?

    In that case I look at a rectangle on the floor from above; then I imagine two equal length (length > diagonal of rectangle) wires, one from A to C and one from B to D. If I lift them with a hook or something, where can I end up with the top of the pyramid ? Can the projection of the tip on the floor be off both symmetry axes or only off one ?
  6. Oct 9, 2015 #5
    Yes, only non horizontal ones. I tried the same but somehow its hard to show anything "mathematically"
  7. Oct 9, 2015 #6


    Staff: Mentor

    You could draw the rectangular base and attach threads to each corner and then pull them up to a common point. This is how I'd visualize it.
  8. Oct 9, 2015 #7
    Me too, I'll try it. But how it can be proven using elementary geometry?
  9. Oct 9, 2015 #8


    Staff: Mentor

    I don't know how to prove it other than starting with the rectangular base and drawing a line segment of a any length perpendicular to the base such that one endpoint is in the rectangle then you can draw a line segment from any vertice of the rectangular base to the free line segment endpoint. Something like that...
  10. Oct 9, 2015 #9
    Ive tried that already but it didnt lead me to anywhere
  11. Oct 9, 2015 #10


    Staff: Mentor

    Are you trying to proof that such a shape exists?
  12. Oct 9, 2015 #11
    I firmly believe that it exists - I did an experiment with strings

    But I cant guarantee it exists
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Is there any pyramid like that?
  1. Square pyramid? (Replies: 4)

  2. Pascal's pyramid (Replies: 1)

  3. Frustum Pyramid (Replies: 3)