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CARTAN'S UMBRELLA
Surface studied by Henri Cartan and Hassler
Whitney in 1957.
Henri Cartan (1904  2008): French mathematician. 
Cartesian equation: .
Cartesian parametrization: . 
Cartan's umbrella is the algebraic surface with the above equation, with the characteristic of having an isolated line (the axis Oz), the handle of the umbrella (cf also Whitney's umbrella).
Cartan's umbrella can be defined as a cone with directrix a cubic of Agnesi. 

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© Robert FERRÉOL
2017