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EXAMPLES

1

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 ...

Ruth Gentry, **1896**

3

The collected mathematical papers of Arthur Cayley: ... 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 ...

1852

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, ...

Rick Miranda, **1995**

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 ...

Robert M. Corless, **2002**

7

Algebraic Geometry
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?) ...

Robin Hartshorne, **1977**

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**

9

Surfaces with K2
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 ...

Ingrid C. Bauer, **2001**

10

Canadian Journal of Mathematics
REFERENCE

« EDUCALINGO. *Tacnode* [online]. Available <https://educalingo.com/en/dic-en/tacnode>. Nov 2019 ».