Vision 4D

Quadratic hypersurfaces

A quadratic hypersurface is the set of points verifying an algebraic equation of degree 2.

This application proposes for you to visualize the following list of quadratic hypersurfaces in the space-time of dimension 4. In the equations, x,y,z are the coordinates of the space, and we use the variable t to designate the coordinate time. A same hypersurface is often presented several times, under different viewing angles (in particular with respect to t).

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Show 1x2+y2+z2+t2=1sphere S3
Show 2x2+y2+z2-t2=0spherical cone with principal axis on the axis of t
Show 3x2+y2-z2+t2=0spherical cone with principal axis on the axis of z
Show 4x2-y2+z2+t2=0spherical cone with principal axis on the axis of y
Show 5x2+y2-zt=0spherical cone whose principal axis is the line x=y=z+t=0
Show 6x2+z2-yt=0spherical cone whose principal axis is the line x=z=y+t=0
Show 7x2+y2+z2-t2=1spherical hyperboloid whose principal axis is the axis of t
Show 8x2+y2-z2+t2=1spherical hyperboloid whose principal axis is the axis of z
Show 9x2-y2+z2+t2=1spherical hyperboloid whose principal axis is the axis of y
Show 10x2+y2-zt=1spherical hyperboloid whose principal axis is the line x=y=z+t=0
Show 11x2+z2-yt=1spherical hyperboloid whose principal axis is the line x=z=y+t=0
Show 12x2+y2-z2-t2=0vertical hyperboloidal cone
Show 13x2-y2+z2-t2=0horizontal hyperboloidal cone
Show 14x2-y2-zt=0hyperboloidal cone
Show 15x2-z2-yt=0hyperboloidal cone
Show 16x2+y2-z2-t2=1hyperboloidal hyperboloid
Show 17x2-y2+z2-t2=1hyperboloidal hyperboloid
Show 18x2+y2-z2-t2= -1hyperboloidal hyperboloid
Show 19x2-y2+z2-t2= -1hyperboloidal hyperboloid
Show 20x2-y2-zt=1hyperboloidal hyperboloid
Show 21x2-z2-yt=1hyperboloidal hyperboloid
Show 22x2+y2+z2-t=0spherical paraboloid oriented towards the axis of t
Show 23x2+y2-z+t2=0spherical paraboloid oriented towards the axis of z
Show 24x2-y+z2+t2=0spherical paraboloid oriented towards the axis of y
Show 25x2+y2-z2-t=0hyperboloidal paraboloid oriented towards the axis of t, vertical
Show 26x2-y2+z2-t=0hyperboloidal paraboloid oriented towards the axis of t, horizontal
Show 27x2+y2-z-t2=0hyperboloidal paraboloid oriented towards the axis of z
Show 28x2-y2-z+t2=0hyperboloidal paraboloid oriented towards the axis of z
Show 29x2-y+z2-t2=0hyperboloidal paraboloid oriented towards the axis of y
Show 30x2-y-z2+t2=0hyperboloidal paraboloid oriented towards the axis of y
Show 31x2+y2+t2=1vertical spherical cylinder
Show 32x2+z2+t2=1horizontal spherical cylinder
Show 33x2+y2-t2=0conic cylinder with a singular line on the axis of z
Show 34x2+z2-t2=0conic cylinder with a singular line on the axis of y
Show 35x2+y2-t2=1hyperboloidal cylinder with one sheet, vertical
Show 36x2+z2-t2=1hyperboloidal cylinder with one sheet, horizontal
Show 37x2+y2-t2= -1hyperboloidal cylinder with two sheets, vertical
Show 38x2+z2-t2= -1hyperboloidal cylinder with two sheets, horizontal

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Description: plots hypersurfaces etc. in space-time of dimension 4. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games

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