Concept
Ellipse
Related concepts (49)
Pencil (geometry)
In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a plane, or the set of circles that pass through two given points in a plane. Although the definition of a pencil is rather vague, the common characteristic is that the pencil is completely determined by any two of its members. Analogously, a set of geometric objects that are determined by any three of its members is called a bundle.
Radius of curvature
In differential geometry, the radius of curvature (Rc), R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. In the case of a space curve, the radius of curvature is the length of the curvature vector. In the case of a plane curve, then R is the absolute value of where s is the arc length from a fixed point on the curve, φ is the tangential angle and κ is the curvature.
Oval
An oval () is a closed curve in a plane which resembles the outline of an egg. The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or two axes of symmetry of an ellipse. In common English, the term is used in a broader sense: any shape which reminds one of an egg. The three-dimensional version of an oval is called an ovoid. The term oval when used to describe curves in geometry is not well-defined, except in the context of projective geometry.
Lissajous curve
A Lissajous curve ˈlɪsəʒuː, also known as Lissajous figure or Bowditch curve ˈbaʊdɪtʃ, is the graph of a system of parametric equations which describe the superposition of two perpendicular oscillations in x and y directions of different angular frequency (a and b). The resulting family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail in 1857 by Jules Antoine Lissajous (for whom it has been named). Such motions may be considered as a particular of kind of complex harmonic motion.
Annulus (mathematics)
In mathematics, an annulus (plural annuli or annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware washer. The word "annulus" is borrowed from the Latin word anulus or annulus meaning 'little ring'. The adjectival form is annular (as in annular eclipse). The open annulus is topologically equivalent to both the open cylinder S1 × (0,1) and the punctured plane.
Conical surface
In geometry, a (general) conical surface is the unbounded surface formed by the union of all the straight lines that pass through a fixed point — the apex or vertex — and any point of some fixed space curve — the directrix — that does not contain the apex. Each of those lines is called a generatrix of the surface. Every conic surface is ruled and developable. In general, a conical surface consists of two congruent unbounded halves joined by the apex.
Steiner inellipse
In geometry, the Steiner inellipse, midpoint inellipse, or midpoint ellipse of a triangle is the unique ellipse inscribed in the triangle and tangent to the sides at their midpoints. It is an example of an inellipse. By comparison the inscribed circle and Mandart inellipse of a triangle are other inconics that are tangent to the sides, but not at the midpoints unless the triangle is equilateral. The Steiner inellipse is attributed by Dörrie to Jakob Steiner, and a proof of its uniqueness is given by Dan Kalman.
Concentric objects
In geometry, two or more objects are said to be concentric when they share the same center. Any pair of (possibly unalike) objects with well-defined centers can be concentric, including circles, spheres, regular polygons, regular polyhedra, parallelograms, cones, conic sections, and quadrics. Geometric objects are coaxial if they share the same axis (line of symmetry). Geometric objects with a well-defined axis include circles (any line through the center), spheres, cylinders, conic sections, and surfaces of revolution.
Steiner ellipse
In geometry, the Steiner ellipse of a triangle, also called the Steiner circumellipse to distinguish it from the Steiner inellipse, is the unique circumellipse (ellipse that touches the triangle at its vertices) whose center is the triangle's centroid. Named after Jakob Steiner, it is an example of a circumconic. By comparison the circumcircle of a triangle is another circumconic that touches the triangle at its vertices, but is not centered at the triangle's centroid unless the triangle is equilateral.
Director circle
In geometry, the director circle of an ellipse or hyperbola (also called the orthoptic circle or Fermat–Apollonius circle) is a circle consisting of all points where two perpendicular tangent lines to the ellipse or hyperbola cross each other. The director circle of an ellipse circumscribes the minimum bounding box of the ellipse. It has the same center as the ellipse, with radius , where and are the semi-major axis and semi-minor axis of the ellipse.