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).
. | N^{o} | equation | description |
---|---|---|---|
Show | 1 | x^{2}+y^{2}+z^{2}+t^{2}=1 | sphere S^{3} |
Show | 2 | x^{2}+y^{2}+z^{2}-t^{2}=0 | spherical cone with principal axis on the axis of t |
Show | 3 | x^{2}+y^{2}-z^{2}+t^{2}=0 | spherical cone with principal axis on the axis of z |
Show | 4 | x^{2}-y^{2}+z^{2}+t^{2}=0 | spherical cone with principal axis on the axis of y |
Show | 5 | x^{2}+y^{2}-zt=0 | spherical cone whose principal axis is the line x=y=z+t=0 |
Show | 6 | x^{2}+z^{2}-yt=0 | spherical cone whose principal axis is the line x=z=y+t=0 |
Show | 7 | x^{2}+y^{2}+z^{2}-t^{2}=1 | spherical hyperboloid whose principal axis is the axis of t |
Show | 8 | x^{2}+y^{2}-z^{2}+t^{2}=1 | spherical hyperboloid whose principal axis is the axis of z |
Show | 9 | x^{2}-y^{2}+z^{2}+t^{2}=1 | spherical hyperboloid whose principal axis is the axis of y |
Show | 10 | x^{2}+y^{2}-zt=1 | spherical hyperboloid whose principal axis is the line x=y=z+t=0 |
Show | 11 | x^{2}+z^{2}-yt=1 | spherical hyperboloid whose principal axis is the line x=z=y+t=0 |
Show | 12 | x^{2}+y^{2}-z^{2}-t^{2}=0 | vertical hyperboloidal cone |
Show | 13 | x^{2}-y^{2}+z^{2}-t^{2}=0 | horizontal hyperboloidal cone |
Show | 14 | x^{2}-y^{2}-zt=0 | hyperboloidal cone |
Show | 15 | x^{2}-z^{2}-yt=0 | hyperboloidal cone |
Show | 16 | x^{2}+y^{2}-z^{2}-t^{2}=1 | hyperboloidal hyperboloid |
Show | 17 | x^{2}-y^{2}+z^{2}-t^{2}=1 | hyperboloidal hyperboloid |
Show | 18 | x^{2}+y^{2}-z^{2}-t^{2}= -1 | hyperboloidal hyperboloid |
Show | 19 | x^{2}-y^{2}+z^{2}-t^{2}= -1 | hyperboloidal hyperboloid |
Show | 20 | x^{2}-y^{2}-zt=1 | hyperboloidal hyperboloid |
Show | 21 | x^{2}-z^{2}-yt=1 | hyperboloidal hyperboloid |
Show | 22 | x^{2}+y^{2}+z^{2}-t=0 | spherical paraboloid oriented towards the axis of t |
Show | 23 | x^{2}+y^{2}-z+t^{2}=0 | spherical paraboloid oriented towards the axis of z |
Show | 24 | x^{2}-y+z^{2}+t^{2}=0 | spherical paraboloid oriented towards the axis of y |
Show | 25 | x^{2}+y^{2}-z^{2}-t=0 | hyperboloidal paraboloid oriented towards the axis of t, vertical |
Show | 26 | x^{2}-y^{2}+z^{2}-t=0 | hyperboloidal paraboloid oriented towards the axis of t, horizontal |
Show | 27 | x^{2}+y^{2}-z-t^{2}=0 | hyperboloidal paraboloid oriented towards the axis of z |
Show | 28 | x^{2}-y^{2}-z+t^{2}=0 | hyperboloidal paraboloid oriented towards the axis of z |
Show | 29 | x^{2}-y+z^{2}-t^{2}=0 | hyperboloidal paraboloid oriented towards the axis of y |
Show | 30 | x^{2}-y-z^{2}+t^{2}=0 | hyperboloidal paraboloid oriented towards the axis of y |
Show | 31 | x^{2}+y^{2}+t^{2}=1 | vertical spherical cylinder |
Show | 32 | x^{2}+z^{2}+t^{2}=1 | horizontal spherical cylinder |
Show | 33 | x^{2}+y^{2}-t^{2}=0 | conic cylinder with a singular line on the axis of z |
Show | 34 | x^{2}+z^{2}-t^{2}=0 | conic cylinder with a singular line on the axis of y |
Show | 35 | x^{2}+y^{2}-t^{2}=1 | hyperboloidal cylinder with one sheet, vertical |
Show | 36 | x^{2}+z^{2}-t^{2}=1 | hyperboloidal cylinder with one sheet, horizontal |
Show | 37 | x^{2}+y^{2}-t^{2}= -1 | hyperboloidal cylinder with two sheets, vertical |
Show | 38 | x^{2}+z^{2}-t^{2}= -1 | hyperboloidal cylinder with two sheets, horizontal |
Other animated plotters: Polyray, Tracés Animés, Polynomial sweep.
Please take note that WIMS pages are interactively generated; they are not ordinary HTML files. They must be used interactively ONLINE. It is useless for you to gather them through a robot program.
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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