-
shape will be the
evolute of that curve. The
evolute of a
circle is
therefore a
single point at its center. Equivalently, an
evolute is the
envelope of...
- used), cubocycloid, and paracycle. It is
nearly identical in form to the
evolute of an ellipse. If the
radius of the
fixed circle is a then the equation...
- \varphi +\cos 3\varphi ,3\sin \varphi +\sin 3\varphi )} (see above). The
evolute of a
curve is the
locus of
centers of curvature. In detail: For a curve...
- of the
circle k {\displaystyle k} , one gets a limaçon of Pascal. The
evolute of a
curve is the
locus of
centers of curvature. In detail: For a curve...
- as the
string is
either unwrapped from or
wrapped around the curve. The
evolute of an
involute is the
original curve. It is
generalized by the roulette...
- An
ellipse (red) and its
evolute (blue). The dots are the
vertices of the ellipse, at the
points of
greatest and
least curvature....
- Mamikon's theorem. The
envelope of the
normals of the
tractrix (that is, the
evolute of the tractrix) is the
catenary (or
chain curve)
given by y = a cosh x/a...
- curvature, form
another curve,
called the
evolute of C.
Vertices of C
correspond to
singular points on its
evolute.
Within any arc of a
curve C
within which...
- the
curve and the
envelope of such
normals is its
evolute. Therefore, YR is
tangent to the
evolute and the
point Y is the foot of the
perpendicular from...
-
typically only have 3-point
contact with
their osculating circle. The
evolute of a
curve will
generically have a cusp when the
curve has a vertex; other...
