Imaginary curve
Encyclopedia
In geometry
an imaginary curve is an algebraic curve
which contains a finite number of real point
s.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
an imaginary curve is an algebraic curve
Algebraic curve
In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with circles and other conic sections.- Plane algebraic curves...
which contains a finite number of real point
Real point
A point in the complex projective plane is called real if there exists a complex number z such that za, zb and zc are all real numbers.This definition can be widened to complex projective space and complex projective hyperspaces as follows:...
s.
See also
- Imaginary pointImaginary pointA point in the complex projective plane is called an imaginary point if there exists no complex number z such that za, zb and zc are real....
- Real pointReal pointA point in the complex projective plane is called real if there exists a complex number z such that za, zb and zc are all real numbers.This definition can be widened to complex projective space and complex projective hyperspaces as follows:...
- Imaginary line (mathematics)Imaginary line (mathematics)In geometry, an imaginary line is a straight line that only contains one real point. It can be proven that this point is the intersection point with the conjugated line.It is a special case of an imaginary curve....
- Real lineReal lineIn mathematics, the real line, or real number line is the line whose points are the real numbers. That is, the real line is the set of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one...
- Real curveReal curveIn geometry a real curve is an algebraic curve that contains an infinite number of real points.-See also:*Imaginary point*Real point*Imaginary line*Real line*Imaginary curve...