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NEWTON TRIDENT
Curve studied by Newton in 1701.
Other name: Cartesian parabola. Isaac Newton (1642-1727): English physicist, mathematician, and astronomer. |
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Cartesian equation: Rational cubic with a double point (at infinity in the direction of Oy), the parabola Reduced Cartesian equation: |
The Newton tridents are defined by the above Cartesian
equation; they can be seen as the medians
along Oy of the parabolas |
![]() The trident as the median of a parabola and a hyperbola. |
They also appear as contour lines of the cubic surface |
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They can also be obtained by hyperbolism
from the cubical parabolas.
Their images by the homographic transformation In the opposite figure, we used |
![]() The Cartesian folium is a perspective of the Newton trident. |
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© Robert FERRÉOL 2017