Some unkonwn words in mathematics - What is Cybernetics? What is Manifold?

What is a Manifold?

The branch of science is concerned with control systems, especially about the comparisons between those of machines and those of man and other animals. In a series of operations, information gained at one stage can be used to modify later performances of that operation. This is known as feedback and enables a control system to check and possibly adjust its actions when required.

What is a cyclic polygon?

 A cyclic polygon is a polygon with all its vertices on the circumference of a circle. All triangles are cyclic, squares and rectangles are cyclic quadrilaterals, and all regular polygons are cyclic.

What is the Impossibility Theorem?

Any theorem asserting the impossibility of some much sought-after is often intuitively plausible.

What is Locus?

The path is traced out by a point constrained to move by given conditions. The locus may be a point, line, curve, plane, surface, or solid. For example, the locus of a point that moves in such a way that its distance from a fixed point is always equal to its distance from a fixed straight line is a parabola.

What is a Manifold?

Manifold is a class with subclasses. For example, a plane is a two-dimensional manifold of points as each point is specified by two coordinates, the abscissa and the ordinate. Similarly, Euclidean space is a three-dimensional manifold of points.

What is Meridian?

Meridian is a great circle passing through the north and south poles. A local meridian of a point on the earth’s surface is the great circle passing through the north and south poles and that point.

What is Orthocenter?

An orthocenter is a point that is the common point of intersection of the three altitudes of a triangle. The altitudes of a triangle are the lines from each vertex drawn perpendicular to the opposite sides. The triangle formed by joining the feet of the altitudes is called a peal triangle.

What is Osborne’s rule?

The rule that states that trigonometric identities can be transformed into the corresponding identities for hyperbolic functions by multiplying out fully, replacing all trigonometric functions with their hyperbolic analogues, and then changing the signs of any terms involving the product of two signs, for instance,

Cos (x-y) = cos x cos y + sin x + sin y

Osborne’s rule permits us to infer

Cosh(x-y) = cosh x cosh y – sinh x sinh y

What is Perimeter?

Perimeter is the length of a plane figure around its edge. For example, the perimeter of a square is four times the length of its side. The length of a closed curve is its perimeter, so that the perimeter of a circle is its circumference.

What is the Pivotal Function?

A function of data, derived from an experiment and the parameter of interest, is regarded as a random variable with probability distribution independent of any unknown parameter.

What is Platonism?

The philosophical theory that mathematical objects exist in advance of and independently of our knowledge of them and of any physical instantiation of them, and therefore that mathematical truth does not consist in, but is the aim of the construction of proofs.  

What is a Polyhedron?

A polyhedron is a solid figure bounded by several faces each of which is a polygon. The point of intersection of three or more faces is called a vertex of the polyhedron; the line of intersection of two plane faces is called an edge of the polyhedron. A regular polyhedron is one in which all the faces are congruent regular polygons. There are only five regular polyhedrons with the number of faces as 4, 6, 8, 12 and 20.