Fully inflated air pillow

It is a fourth order surface where sections parallel x- , y - axes are
ellipses of variable eccentricity,and a constant major axis. The foci
move from center of square (case of circle) to corners (narrow digon
line ellipse) along diagonals of square .The x =y sections are
parabolas It looks like a fully inflated square pillow whose surface
equation is a^2 z^2 = ( a^2 - x^2) (a^2 - y^2) and the image written
in Mathematica is:

a = 1; ContourPlot3D[ z^2 == a^2 - (x^2 + y^2) + ( x y /a)^2 , {x, -
a, a}, {y, -a, a}, {z, -a, a}]

May be known already but hope it is interesting.

Narasimham
.

Relevant Pages

  • Re: Fully inflated air pillow
    ... ellipses of variable eccentricity,and a constant major axis. ... move from center of square to corners (narrow digon ... line ellipse) along diagonals of square .The x =y sections are ...
    (sci.math)
  • Re: Fully inflated air pillow
    ... y - axes are ellipses of variable ... eccentricity,and a constant major axis. ... square to corners along ...
    (sci.math)