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TACNODE

Tacnode

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

In classical algebraic geometry, a tacnode (also called a point of osculation or double cusp) is a kind of singular point of a curve. It is defined as

Tacnode

List of curves topics

Singular solution Sinuosity Slope Space curve Spinode Square wheel Subtangent Tacnode Tangent Tangent space Tangential angle Torsion of curves Trajectory Transcendental

List of curves topics

List_of_curves_topics

Kurt Johansson (mathematician)

Swedish mathematician

Johansson, Kurt; Van Moerbeke, Pierre (2014). "Double Aztec diamonds and the tacnode process". Advances in Mathematics. 252: 518–571. arXiv:1112.5532. doi:10

Kurt Johansson (mathematician)

Kurt_Johansson_(mathematician)

Cusp (singularity)

Point on a curve where motion must move backwards

not divide P1 then we have type exactly A3 (the zero-level-set here is a tacnode). If x1 divides P1 we complete the square on x 1 2 + P 1 {\displaystyle

Cusp (singularity)

Cusp_(singularity)

List of Latin words with English derivatives

internode, nodal, node, nodose, nodosity, nodular, nodule, nodulose, tacnode †nodulus nodul- nomen nomin- name agnomen, agnominal, agnomination, binomen

List of Latin words with English derivatives

List_of_Latin_words_with_English_derivatives

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

nodosity, nodular, nodulation, nodule, nodulose, nodulus, nodus, supernode, tacnode, trinodal, uninodal nom- arrangement, law, order Greek νόμος (nómos), νομή

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

List_of_Greek_and_Latin_roots_in_English/H–O

Acnode

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

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

Acnode

Singular point of a curve

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

x 3 − y 2 = 0 , {\displaystyle x^{3}-y^{2}=0,} also called a spinode A tacnode: x 4 − y 2 = 0 {\displaystyle x^{4}-y^{2}=0} A rhamphoid cusp: x 5 − y

Singular point of a curve

Singular_point_of_a_curve

Crunode

Point where a curve intersects itself at an angle

^{2}f}{\partial x~\partial y}}\right)^{2}<0.} Singular point of a curve Acnode Cusp Tacnode Saddle point Salmon, George (1879). A treatise on the higher plane curves:

Crunode

Glossary of classical algebraic geometry

of a module or sheaf. tacnode A tacnode is a point of a curve where two branches meet in the same direction. (Cayley 1852) tacnode-cusp A singularity of

Glossary of classical algebraic geometry

Glossary_of_classical_algebraic_geometry

List of Greek and Latin roots in English/N

nodosity, nodular, nodulation, nodule, nodulose, nodulus, nodus, supernode, tacnode, trinodal, uninodal nom- arrangement, law, order Greek νόμος (nómos), νομή

List of Greek and Latin roots in English/N

List_of_Greek_and_Latin_roots_in_English/N