René de Sluze (1622,1685): Belgian cleric and mathematician. Other name: conchoid of Sluze (because of its similarity to the conchoid of Nicomedes, but it is not a conchoid).

 

Polar equation: . Cartesian equation: . Right rational circular cubic with isolated point.

The Sluze cubic associated to a line (D₀) (here, the line x = a) and a pole O is the locus of the points M on the line (OM₀) such that , when M₀ describes (D₀).

We obtain this way all the right rational circular cubics located on the other side of the singularity, with respect to the asymptote (including the visiera).
In the construction above, if  is replaced by  , (which gives the polar equation ), we obtain all the other right rational circular cubics, including the cissoid of Nicomedes, the Mac-Laurin trisectrix, the right strophoid.
 
 

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© Robert FERRÉOL  2017