Ads
related to: dual curve in geometry examples worksheet 1 answers sheetstudy.com has been visited by 100K+ users in the past month
Search results
Results From The WOW.Com Content Network
If the degree of the curve is d then the degree of the polar is d − 1 and so the number of tangents that can be drawn through the given point is at most d(d − 1). The dual of a line (a curve of degree 1) is an exception to this and is taken to be a point in the dual space (namely the original line).
A curve in this context is defined by a non-degenerate algebraic equation in the complex projective plane. Lines in this plane correspond to points in the dual projective plane and the lines tangent to a given algebraic curve C correspond to points in an algebraic curve C * called the dual curve.
dual 1. The dual of a projective space is the set of hyperplanes, considered as another projective space. 2. The dual curve of a plane curve is the set of its tangent lines, considered as a curve in the dual projective plane. 3. A dual number is a number of the form a+εb where ε has square 0. Semple & Roth (1949, p.268)
In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A.
These sets can be used to define a plane dual structure. Interchange the role of "points" and "lines" in C = (P, L, I) to obtain the dual structure. C ∗ = (L, P, I ∗), where I ∗ is the converse relation of I. C ∗ is also a projective plane, called the dual plane of C. If C and C ∗ are isomorphic, then C is called self-dual.
1.3 Curves with genus greater than one. 1.4 Curve families with variable genus. 2 Transcendental curves. Toggle Transcendental curves subsection. 2.1 Spirals.
Regular polygons are self-dual. The dual of an isogonal (vertex-transitive) polygon is an isotoxal (edge-transitive) polygon. For example, the (isogonal) rectangle and (isotoxal) rhombus are duals. In a cyclic polygon, longer sides correspond to larger exterior angles in the dual (a tangential polygon), and shorter sides to smaller angles.
Bézout's theorem is a statement in algebraic geometry concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that in general the number of common zeros equals the product of the degrees of the polynomials. [1] It is named after Étienne Bézout.