What are the conics of Apollonius?
Apollonius has in mind, of course, the conic sections, which he describes in often convolute language: “a curve in the same plane” is a circle, ellipse or parabola, while “two curves in the same plane” is a hyperbola. These figures are the circle, ellipse, and two-branched hyperbola.
What did Apollonius of Perga discover?
Apollonius of Perga (c. 262–190 bc), known as the “Great Geometer,” gave the conic sections their names and was the first to define the two branches of the hyperbola (which presuppose the double cone).
What is the meaning of degenerate conics?
In geometry, a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve. For any degenerate conic in the real plane, one may choose f and g so that the given degenerate conic belongs to the pencil they determine.
What are the three types of degenerate conics?
A degenerate conic is generated when a plane intersects the vertex of the cone. There are three types of degenerate conics: a single point, a line or two parallel lines, or two intersecting lines.
Why are they called conics?
Description. Hyperbola, ellipse, and parabola are together known as conic sections, or just conics. So called because they are the intersection of a right circular cone and a plane.
What was Apollonius famous for?
Apollonius was a Greek mathematician known as ‘The Great Geometer’. His works had a very great influence on the development of mathematics and his famous book Conics introduced the terms parabola, ellipse and hyperbola.
How do you classify degenerate conics?
There are three types of degenerate conics:
- A singular point, which is of the form: (x−h)2a+(y−k)2b=0.
- A line, which has coefficients A=B=C=0 in the general equation of a conic.
- A degenerate hyperbola, which is of the form: (x−h)2a−(y−k)2b=0.
What is a degenerate equation?
In mathematics, something is called degenerate if it is a special case of an object which has, in some sense, “collapsed” into something simpler. For example, the equation x2+y2=0 can be thought of as a degenerate circle, while x2−y2=0 is a degenerate hyperbola: it gives the two straight lines y=x and y=−x.
What are degenerate equations?
What are the five identified conics?
According to the different positions of the cutting plane, there arise five different figures or sections, namely, a triangle, a circle, an ellipse, a parabola, and an hyperbola: the three last of which only are peculiarly called conic sections.
What do you mean by conics?
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type.