This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous in 1857.
12.
In the early 1890s he published three famous papers, including one with the first use of the characteristic linear series of a family of curves.
13.
However, 4th-order contact can occur generically in a 1-parameter family of curves, where two vertices ( one maximum and one minimum ) come together and annihilate.
14.
All other points flow along a certain family of curves, " away " from the first fixed point and " toward " the second fixed point.
15.
A "'pseudoline arrangement "'is a family of curves that share similar complete for the existential theory of the reals to distinguish stretchable arrangements from non-stretchable ones.
16.
Near points where the gradient of " u " ( or, equivalently, " v " ) is not zero, these families form an orthogonal family of curves.
17.
They move all other points away from the South pole and toward the North pole ( or vice versa ), along a family of curves called "'loxodromes " '.
18.
In geometry, a "'lima�on trisectrix "'( called simply a "'trisectrix "'by some authors ) is a member of the Lima�on family of curves which has the trisectrix, or angle trisection, property.
19.
Families of curves appear frequently in solutions of differential equations; when an additive constant of integration is introduced, it will usually be manipulated algebraically until it no longer represents a simple linear transformation.
20.
Note that with this formula, if g is a function of three variables its level sets are surfaces, and the family of curves \ vec r ( t ) are orthogonal to the surfaces.
