Circle

A circle is a simple shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius.

A circle is a simple closed curve which divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a disk.

A circle may also be defined as a special ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations.

Terminology

Circle (2014 film)

Circle (Turkish: Daire) is a 2014 film written and directed by director Atil Inac.

Plot

In the hard-boiled world, where will the soft-shelled end up? A cozy kind of extermination is on the stage and keeping a low profile. The decadence around us is nothing less than clandestine annihilation of the civil man. Yet it is carried out so well with a grinning face, it is officially sold as transition. Now that the tamed indulgent is striped off social justice, welfare, even denied the tender love of concentration camps and slavery plantations of past centuries. At least hand them a round of rope… They have high expectations from taking things in their own hands.

Circle is a peculiar story of an ordinary man caught between an untimely romance and brave new hostile world.

Characters

Awards

Circle (Eddie Izzard)

Circle is the name of a stand-up tour by the comedian Eddie Izzard in 2000.

It was released on VHS and DVD in the United Kingdom on 18 November 2002. The video includes Eddie performing a French version of his show with English subtitles.

The performance features many of Izzard's traditional themes, particularly religion (or "philosophies with some good ideas, and some fucking weird ones"). A discussion about Jesus' role in the three main Abrahamic faiths sees him "waiting offstage" in Judaism and playing on the same sporting team as Muhammad in Islam. This is counterpointed with a dialogue between a Crusader and his enemy in which both men are trying to kill the other "in the name of Jesus". He also mentions his impression that in Buddhism, Jesus is "Buddha's baby brother Benny".

The rigidity of religion is also lampooned, particularly as it relates to the Renaissance. Galileo's persecution by the Catholic Church is mentioned, although the man is eventually asked (in prison) "Galileo, Galileo, will you do the fandango?"

Functional (C++)

In the context of the C++ programming language, functional refers to a header file that is part of the C++ Standard Library and provides a number of predefined class templates for function objects, including arithmetic operations, comparisons, and logical operations. Instances of these class templates are C++ classes that define a function call operator, and the instances of these classes can be called as if they were functions. It is possible to perform very sophisticated operations without actually writing a new function object, simply by combining predefined function objects and function object adaptors.

The class template std::function provided by C++11 is a general-purpose polymorphic function wrapper. Instances of std::function can store, copy, and invoke any callable target—functions, lambda expressions (expressions defining anonymous functions), bind expressions (instances of function adapters that transform functions to other functions of smaller arity by providing values for some of the arguments), or other function objects.

Functional (mathematics)

In mathematics, and particularly in functional analysis and the calculus of variations, a functional is a function from a vector space into its underlying scalar field, or a set of functions of the real numbers. In other words, it is a function that takes a vector as its input argument, and returns a scalar. Commonly the vector space is a space of functions, thus the functional takes a function for its input argument, then it is sometimes considered a function of a function (a higher-order function). Its use originates in the calculus of variations where one searches for a function that minimizes a certain functional. A particularly important application in physics is searching for a state of a system that minimizes the energy functional.

Functional details

Duality

The mapping

is a function, where x₀ is an argument of a function f. At the same time, the mapping of a function to the value of the function at a point

is a functional, here x₀ is a parameter.

Provided that f is a linear function from a linear vector space to the underlying scalar field, the above linear maps are dual to each other, and in functional analysis both are called linear functionals.