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CRUNODE

Crunode

Point where a curve intersects itself at an angle

In mathematics, a crunode (archaic; from Latin crux "cross" + node) or node of an algebraic curve is a type of singular point at which the curve intersects

Crunode

Singular point of a curve

Point on a curve not given by a smooth embedding of a parameter

, {\displaystyle c_{0}c_{2}-c_{1}^{2}<0,} then the origin is called a crunode. The curve in this case crosses itself at the origin and has two distinct

Singular point of a curve

Singular_point_of_a_curve

Ampersand curve

Type of quartic plane curve

19x^{2}-11xy^{2}-3y^{2}=0.} The graph of the ampersand curve has three crunode points where it intersects itself at (0,0), (1,1), and (1,−1). The curve

Ampersand curve

Ampersand_curve

List of curves topics

concavity Conchoid (mathematics) Confocal Contact (mathematics) Contour line Crunode Cubic Hermite curve Curvature Curve orientation Curve fitting Curve-fitting

List of curves topics

List_of_curves_topics

Cubic plane curve

Type of mathematical curve

ordinary double point. Over the reals, such an ordinary point may be either a crunode if the two tangent lines are real, or an acnode if they are complex conjugate

Cubic plane curve

Cubic_plane_curve

Conchoid of de Sluze

Family of algebraic curves of the form r = sec(θ) + a*cos(θ)

0). The point most distant from the asymptote is (1 + a, 0). (0,0) is a crunode for a < −1. The area between the curve and the asymptote is, for a ≥ −1

Conchoid of de Sluze

Conchoid_of_de_Sluze

List of Latin words with English derivatives

annihilate, annihilation, annihilator, nihil, nil nodus nod- knot acnode, crunode, denouement, internodal, internode, nodal, node, nodose, nodosity, nodular

List of Latin words with English derivatives

List_of_Latin_words_with_English_derivatives

Acnode

Isolated point in the solution set of a polynomial equation in two real variables

minimum or a local maximum at the singularity. Singular point of a curve Crunode Cusp Tacnode Hazewinkel, M. (2001) [1994], "Acnode", Encyclopedia of Mathematics

Acnode

List of Greek and Latin roots in English/H–O

notturno, seminocturnal, trinoctial nod- knot Latin nodus acnode, binodal, crunode, denouement, extranodal, internodal, internode, intranodal, multinodal

List of Greek and Latin roots in English/H–O

List_of_Greek_and_Latin_roots_in_English/H–O

Cassini oval

Class of quartic plane curves

shape of a sideways figure eight with a double point (specifically, a crunode) at the origin. When e > 1, the curve is a single, connected loop enclosing

Cassini oval

Cassini_oval

Algebraic curve

Curve defined as zeros of polynomials

, this is Acnode Bézout's theorem Cramer's theorem (algebraic curves) Crunode Curve Curve sketching Jacobian variety Klein quartic List of curves Hilbert's

Algebraic curve

Algebraic_curve

Tschirnhausen cubic

Cubic plane curve

{\displaystyle ar^{2}=p^{3}} . It has a single self-crossing (a node or crunode), so that an arc of the curve starting and ending at the node forms a bounded

Tschirnhausen cubic

Tschirnhausen_cubic

Evolute

Centers of curvature of a curve

at least d ( 2 d − 3 ) {\displaystyle d(2d-3)} . The maximal number of crunodes (real transverse self-intersections) on the evolute and on its dual curve

Evolute

Domenico Montesano

Italian mathematician (1863–1930)

Togliatti surface, a quintic surface with 31 crunodes (the maximum possible)

Domenico Montesano

Domenico_Montesano

Tacnode

Point on a curve at which two or more osculating circles are tangent

the required diffeomorphism of the normal forms. Acnode Cusp or Spinode Crunode Schwartzman, Steven (1994), The Words of Mathematics: An Etymological Dictionary

Tacnode

List of Greek and Latin roots in English/N

notturno, seminocturnal, trinoctial nod- knot Latin nodus acnode, binodal, crunode, denouement, extranodal, internodal, internode, intranodal, multinodal

List of Greek and Latin roots in English/N

List_of_Greek_and_Latin_roots_in_English/N

Strophoid

Geometric curve constructed from another curve and two points

curve and, by the expression in polar coordinates it is rational. It has a crunode at (0, 0) and the line y = b is an asymptote. Putting α = π / 2 {\displaystyle

Strophoid

Inverse curve

Curve created by a geometric operation

the original curve is a hyperbola and the inverse forms two loops with a crunode at the origin. The general equation of an ellipse or hyperbola is x 2 a

Inverse curve