Bow curve
Encyclopedia
In mathematics
, the bow curve is a quartic plane curve
with the equation:
The bow curve has a single triple point at x=0, y=0, and consequently is a rational curve, with genus
zero.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the bow curve is a quartic plane curve
Quartic plane curve
A quartic plane curve is a plane curve of the fourth degree. It can be defined by a quartic equation:Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0....
with the equation:
The bow curve has a single triple point at x=0, y=0, and consequently is a rational curve, with genus
Geometric genus
In algebraic geometry, the geometric genus is a basic birational invariant pg of algebraic varieties and complex manifolds.-Definition:...
zero.