A quartic plane curve is a plane curve of the fourth degree. It can be defined by a quartic equation:
This equation has fifteen constants. However, it can be multiplied by any non-zero constant without changing the curve. Therefore, the space of quartic curves can be identified with the real projective space . It also follows that there is exactly one quartic curve that passes through a set of fourteen distinct points in general position, since a quartic has 14 degrees of freedom.
A quartic curve can have a maximum of:
- Four connected components
- Twenty-eight bi-tangents
- Three ordinary double points.
Read more about Quartic Plane Curve: Examples
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—Henry David Thoreau (1817–1862)
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In curve and voice and eye
Despise the human span
Of durance—that is I;
The eternal thing in man,
That heeds no call to die.”
—Thomas Hardy (1840–1928)