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- Tetraview abstract "A tetraview is an attempt to graph a complex function of a complex variable, by a method invented by Davide P. Cervone.A graph of a real function of a real variable is the set of ordered pairs (x,y) such that y = f(x). This is the ordinary two-dimensional Cartesian graph studied in school algebra.Every complex number has both a real part and an imaginary part, so one complex variable is two-dimensional and a pair of complex variables is four-dimensional. A tetraview is an attempt to give a picture of a four-dimensional object using a two-dimensional representation—either on a piece of paper or on a computer screen, showing a still picture consisting of five views, one in the center and one at each corner. This is roughly analogous to a picture of a three-dimensional object by giving a front view, a side view, and a view from above.A picture of a three-dimensional object is a projection of that object from three dimensions into two dimensions. A tetraview is set of five projections, first from four dimensions into three dimensions, and then from three dimensions into two dimensions.A complex function w = f(z), where z = a + bi and w = c + di are complex numbers, has a graph in four-space (four dimensional space) R4 consisting of all points (a, b, c, d) such that c + di = f(a + bi).To construct a tetraview, we begin with the four points (1,0,0,0), (0, 1, 0, 0), (0, 0, 1, 0), and (0, 0, 0, 1), which are vertices of a spherical tetrahedron on the unit three-sphere S3 in R4.We project the four-dimensional graph onto the three-dimensional sphere along one of the four coordinate axes, and then give a two-dimensional picture of the resulting three-dimensional graph. This provides the four corner graph. The graph in the center is a similar picture "taken" from the point of view of the origin.".
- Tetraview wikiPageExternalLink tetra-Z3.html.
- Tetraview wikiPageExternalLink tetra-exp.html.
- Tetraview wikiPageID "2607053".
- Tetraview wikiPageLength "2284".
- Tetraview wikiPageOutDegree "20".
- Tetraview wikiPageRevisionID "626981548".
- Tetraview wikiPageWikiLink 3-sphere.
- Tetraview wikiPageWikiLink 3D_projection.
- Tetraview wikiPageWikiLink Algebra.
- Tetraview wikiPageWikiLink Cartesian_coordinate_system.
- Tetraview wikiPageWikiLink Category:Functions_and_mappings.
- Tetraview wikiPageWikiLink Complex-valued_function.
- Tetraview wikiPageWikiLink Complex_analysis.
- Tetraview wikiPageWikiLink Complex_function.
- Tetraview wikiPageWikiLink Complex_number.
- Tetraview wikiPageWikiLink Complex_variable.
- Tetraview wikiPageWikiLink Coordinate_axis.
- Tetraview wikiPageWikiLink Coordinate_system.
- Tetraview wikiPageWikiLink Davide_P._Cervone.
- Tetraview wikiPageWikiLink Dimension.
- Tetraview wikiPageWikiLink Function_of_a_real_variable.
- Tetraview wikiPageWikiLink Graph_of_a_function.
- Tetraview wikiPageWikiLink Imaginary_part.
- Tetraview wikiPageWikiLink Ordered_pair.
- Tetraview wikiPageWikiLink Real-valued_function.
- Tetraview wikiPageWikiLink Real_function.
- Tetraview wikiPageWikiLink Real_part.
- Tetraview wikiPageWikiLink Set_(mathematics).
- Tetraview wikiPageWikiLink Tetrahedron.
- Tetraview wikiPageWikiLink Three-dimensional_graph.
- Tetraview wikiPageWikiLink Three-sphere.
- Tetraview wikiPageWikiLinkText "Tetraview".
- Tetraview hasPhotoCollection Tetraview.
- Tetraview subject Category:Functions_and_mappings.
- Tetraview hypernym Attempt.
- Tetraview type MilitaryConflict.
- Tetraview type Function.
- Tetraview type Relation.
- Tetraview comment "A tetraview is an attempt to graph a complex function of a complex variable, by a method invented by Davide P. Cervone.A graph of a real function of a real variable is the set of ordered pairs (x,y) such that y = f(x). This is the ordinary two-dimensional Cartesian graph studied in school algebra.Every complex number has both a real part and an imaginary part, so one complex variable is two-dimensional and a pair of complex variables is four-dimensional.".
- Tetraview label "Tetraview".
- Tetraview sameAs m.07rb99.
- Tetraview sameAs Q7706772.
- Tetraview sameAs Q7706772.
- Tetraview wasDerivedFrom Tetraview?oldid=626981548.
- Tetraview isPrimaryTopicOf Tetraview.