Every complex number has both a real part and an imaginary part, so one complex variable is two-dimensional and a BBC 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, this, article, technical, most, readers, understand, please, help, improve, make, understandable, experts, without, removing, technical, details, february, 2024, learn, when, remove, this, message, tetraview, attempt, graph, complex, function, compl. This article may be too technical for most readers to understand Please help improve it to make it understandable to non experts without removing the technical details February 2024 Learn how and when to remove this message 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 BBC 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 External links edithttp www math union edu dpvc professional art tetra exp html Retrieved from https en wikipedia org w index php title Tetraview amp oldid 1205811265, wikipedia, wiki, book, books, library,
