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
Famous quotes containing the words plane and/or curve:
“Even though I had let them choose their own socks since babyhood, I was only beginning to learn to trust their adult judgment.. . . I had a sensation very much like the moment in an airplane when you realize that even if you stop holding the plane up by gripping the arms of your seat until your knuckles show white, the plane will stay up by itself. . . . To detach myself from my children . . . I had to achieve a condition which might be called loving objectivity.”
—Anonymous Parent of Adult Children. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 5 (1978)
“And out again I curve and flow
To join the brimming river,
For men may come and men may go,
But I go on forever.”
—Alfred Tennyson (1809–1892)