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CIRCULAR ALGEBRAIC CURVE

An algebraic curve is said to be *circular* if it passes through points called "cyclic points", with homogeneous coordinates (1, *i*, 0) and (1, –*i*, 0), in the complex projective completion of the plane. In other words, they contain the points at infinity of the two complex lines, called isotropic lines, of equation , the reunion of which is the circle with non-zero radius: .

The necessary and sufficient condition on the affine Cartesian equation is that the polynomial composed of the terms of highest degree be divisible by
. This notion is Euclidian (i.e. invariant by change of orthonormal basis).

The circle is the only circular conic.

See circular cubics for the case of cubics.

See multicircular curves for a generalisation.

See bispherical surface for the 3D analogue.

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© Robert FERRÉOL
2017