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High Quality Content by WIKIPEDIA articles! In geometry, a tacnode is a kind of singular point of a curve. It is defined as a point where two (or more) osculating circles to the curve at that point are tangent.
Jesse Russell, Ronald Cohn,
2012
2
On the forms of plane quartic curves ...
quartic with three dps, of which two may form a tacnode, can all be real with real
contacts; Doppelpunkt is evidently to be translated. crunode; when all three dps
are acnodes one of the four dts is necessarily isolated ; further, when the quartic ...
3
The collected mathematical papers of Arthur Cayley: ...
Tacnode: defined, n, 28—32, v, 266. Tactic : and algebra, v, 293 — 4 ; the term, xi
, 443 ; (see also Arrangements, Groups). Tactinvariant : of two quantics, n, 320 ;
the term, v, 305. Tactions: analytical solution, m, 255 — 7; formulae, iv, 510 — 2; ...
Arthur Cayley, Andrew Russell Forsyth,
1898
4
The Cambridge and Dublin Mathematical Journal
Of course at the tacnode, the tacnode-tangent touches the flecnode-curve.
Passing next to the spinode-curve, the spinode-plane and the tangent-plane at a
consecutive point along the spinode- tangent are identical,* or their line of
intersection ...
5
Algebraic Curves and Riemann Surfaces
A (2, 4)-monomial singularity is a tacnode. A (2, 5)-monomial singularity is called
a higher-order cusp, as are all (2,m)- monomial singularities with m > 5 and odd.
A (2, 6)-monomial singularity is called a higher-order tacnode, as are all (2, ...
6
Essential Maple 7: An Introduction for Scientific Programmers
Figure 2.39: The tacnode curve as produced by plot real curve tion of a
differential equation following paths from halfway between each critical point. The
numerical solution is quite fast, and when solve succeeds the location of critical
points ...
Using (b) we see that the tacnode can be resolved by two successive blowings-
up. (d) Let y be the plane curve v3 = x5, which has a "higher order cusp" at 0.
Show that O is a triple point: that blowing up 0 gives rise to a double point (what
kind?) ...
8
Spinors and Space-Time: Volume 2, Spinor and Twistor Methods ...
A degenerate form of node - called a cusp - can also occur where the tangents to
the two branches coincide, but where, in contrast to the case of a tacnode, there
is only one branch to the curve at the point, not two (see Fig. 8-6fc). Nodes ...
Roger Penrose, Wolfgang Rindler,
1988
Furthermore, let E C P3 be a surface of degree six having as only singularities (
apart from rational double points) C as double curve and having an (ordinary)
tacnode o(£ C) contained in the plane 7, whose tacnodal plane is a. We recall
that ...
10
Canadian Journal of Mathematics
with a tacnode; the curve h = 0 is contracted into the tacnode (whose first
neighbourhood is a double line with four pinch points, image of h = 0) and the
four points in which a meets the quartic curve h = 0 are dilated into lines, which
form the ...