-
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...
- 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...
- 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...
- 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...
- all the
osculating circles (also
called "centers of curvature") is the
evolute of the curve. If the
derivative of
curvature κ'(t) is zero, then the osculating...
- \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...
-
correspond to the
cusps of its
evolute, the
curve formed by the
centers of
curvature of the
given curve. Thus, the
evolute of any
smooth closed curve has...
- 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...
- Anahoplites).
Where it does not
cover those preceding, the
specimen is said to be
evolute (e.g., Dactylioceras). A thin
living tube
called a
siphuncle p****ed through...
- An
ellipse (red) and its
evolute (blue). The dots are the
vertices of the ellipse, at the
points of
greatest and
least curvature....
