Search results
Results from the WOW.Com Content Network
In geometry, a Cassini oval is a quartic plane curve defined as the locus of points in the plane such that the product of the distances to two fixed points is constant. This may be contrasted with an ellipse , for which the sum of the distances is constant, rather than the product.
He defined the oval as the solution to a differential equation, constructed its subnormals, and again investigated its optical properties. [ 8 ] The French mathematician Michel Chasles discovered in the 19th century that, if a Cartesian oval is defined by two points P and Q , then there is in general a third point R on the same line such that ...
Implicit means that the equation is not expressed as a solution for either x in terms of y or vice versa. If F ( x , y ) {\displaystyle F(x,y)} is a polynomial in two variables, the corresponding curve is called an algebraic curve , and specific methods are available for studying it.
Hippopede (red) given as the pedal curve of an ellipse (black). The equation of this hippopede is: + = (+) In geometry, a hippopede (from Ancient Greek ἱπποπέδη (hippopédē) 'horse fetter') is a plane curve determined by an equation of the form
The term oval when used to describe curves in geometry is not well-defined, except in the context of projective geometry. Many distinct curves are commonly called ovals or are said to have an "oval shape". Generally, to be called an oval, a plane curve should resemble the outline of an egg or an ellipse. In particular, these are common traits ...
1 Equation. 2 Developments. 3 See also. 4 References. 5 External links. Toggle the table of contents. Butterfly curve (transcendental) 10 languages. Català ...
The circle with center at Q and with radius R is called the osculating circle to the curve γ at the point P. If C is a regular space curve then the osculating circle is defined in a similar way, using the principal normal vector N. It lies in the osculating plane, the plane spanned by the tangent and principal normal vectors T and N at the ...
The evolute of a curve (in this case, an ellipse) is the envelope of its normals. In the differential geometry of curves , the evolute of a curve is the locus of all its centers of curvature . That is to say that when the center of curvature of each point on a curve is drawn, the resultant shape will be the evolute of that curve.