Search results
Results From The WOW.Com Content Network
In mathematics, the matrix representation of conic sections permits the tools of linear algebra to be used in the study of conic sections. It provides easy ways to calculate a conic section's axis , vertices , tangents and the pole and polar relationship between points and lines of the plane determined by the conic.
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola , the parabola , and the ellipse ; the circle is a special case of the ellipse, though it was sometimes considered a fourth type.
Equivalently, an elementary cube is any translate of a unit cube [,] embedded in Euclidean space (for some , {} with ). [3] A set X ⊆ R d {\displaystyle X\subseteq \mathbf {R} ^{d}} is a cubical complex (or cubical set ) if it can be written as a union of elementary cubes (or possibly, is homeomorphic to such a set).
Menaechmus (Greek: Μέναιχμος, c. 380 – c. 320 BC) was an ancient Greek mathematician, geometer and philosopher [1] born in Alopeconnesus or Prokonnesos in the Thracian Chersonese, who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube using the ...
The trace (purple) of the tangents of a conical spiral with a hyperbolic spiral as floor plan. The black line is the asymptote of the hyperbolic spiral. The collection of intersection points of the tangents of a conical spiral with the --plane (plane through the cone's apex) is called its tangent trace.
Conics, also known as conic sections to emphasize their three-dimensional geometry, arise as the intersection of a plane with a cone. Degeneracy occurs when the plane contains the apex of the cone or when the cone degenerates to a cylinder and the plane is parallel to the axis of the cylinder. See Conic section#Degenerate cases for details.
In general, a conical surface consists of two congruent unbounded halves joined by the apex. Each half is called a nappe, and is the union of all the rays that start at the apex and pass through a point of some fixed space curve. [2] Sometimes the term "conical surface" is used to mean just one nappe. [3]
The analytic determination of the intersection curve of two surfaces is easy only in simple cases; for example: a) the intersection of two planes, b) plane section of a quadric (sphere, cylinder, cone, etc.), c) intersection of two quadrics in special cases. For the general case, literature provides algorithms, in order to calculate points of ...