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View search results from all Wolfram sites (8635 matches)The curvature and torsion functions along a space curve determine it up to an orientation-preserving isometry.
Two unit-speed plane curves which have the same curvature differ only by a Euclidean motion.
If two single-valued continuous functions kappa(s) (curvature) and tau(s) (torsion) are given for s>0, then there exists exactly one space curve, determined except for ...
A Jordan curve is a plane curve which is topologically equivalent to (a homeomorphic image of) the unit circle, i.e., it is simple and closed. It is not known if every Jordan ...
As shown by Schnirelman (1944), a square can be inscribed in any closed convex curve, although it is not known if this holds true for every Jordan curve (Steinhaus 1999, p. ...
A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...
An entire Cremona transformation is a birational transformation of the plane. Cremona transformations are maps of the form x_(i+1) = f(x_i,y_i) (1) y_(i+1) = g(x_i,y_i), (2) ...
A superellipse is a curve with Cartesian equation |x/a|^r+|y/b|^r=1, (1) first discussed in 1818 by Lamé. A superellipse may be described parametrically by x = acos^(2/r)t ...
A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...
The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...
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