next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |

NEWTON TRIDENT

Curve studied by Newton in 1701.
Other name: Cartesian parabola. Isaac Newton (1642-1727): English physicist, mathematician, and astronomer. |

Cartesian equation:
where P is a polynomial of degree 3 with valuation 0
Rational cubic with a double point (at infinity in the direction of Oy),
the parabola
and the hyperbola
are asymptotes.
Reduced Cartesian equation:
(case |

The Newton tridents are defined by the above Cartesian
equation; they can be seen as the medians
along Oy of the parabolas
and the hyperbolas . |
The trident as the median of a parabola and a hyperbola. |

They also appear as contour lines of the cubic surface . |

They can also be obtained by hyperbolism
from the cubical parabolas.

Their images by the homographic transformation
are the curves
which have their double point at O. For example, the trident
is transformed into a Cartesian
folium.
In the opposite figure, we used instead of for the sake of readability. |
The Cartesian folium is a perspective of the Newton trident. |

next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |

© Robert FERRÉOL 2017