When any two curves touch each other at a single point, are they called intersecting, or just called they are touching each other? Are these terms – intersecting curves and touching curves used interchangeably? Is there any difference between these terms?
[Math] When two curves touch each other at a single point, are they called intersecting
analytic geometrycurvesterminology
Related Solutions
These are called $k$-ellipses.
Yes, there is a literature.
Here is one 2007 reference, which can
lead you to others: "Semidefinite Representation of the $k$-Ellipse,"
arXiv:math/0702005v1:
Caveat emptor: The Zariski closure of the 5-ellipse is an algebraic curve
of degree 32(!). See their Fig.5:
There is a temporal element to intercept which is absent from intersect: if two paths are generated respectively by two particles moving through space, the paths may intersect; however, one particle only intercepts the other if they arrive at the point of intersection simultaneously.
Best Answer
An intersection between two curves is a point they both have in common. We say that two curves intersect if they have (at least) one point in common.
Two curves "touching" usually means they are intersecting and at the same time directions of the two curves at the point of intersection are exactly the same.