Focus (geometry)

In geometry, the foci (/ˈfoʊsaɪ/; singular focus) are one or more special points with reference to which any of a variety of curves is constructed. For example, one or two foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola. In addition, two foci are used to define the Cassini oval and the Cartesian oval, and more than two foci are used in defining an n-ellipse.

Conic sections

Defining conics in terms of two foci

An ellipse can be defined as the locus of points for each of which the sum of the distances to two given foci is a constant.

A circle is the special case of an ellipse in which the two foci coincide with each other. Thus, a circle can be more simply defined as the locus of points each of which is a fixed distance from a single given focus. A circle can also be defined as the circle of Apollonius, in terms of two different foci, as the set of points having a fixed ratio of distances to the two foci.

A parabola is a limiting case of an ellipse in which one of the foci is a point at infinity.

Focus

Focus, FOCUS, or foci may refer to:

In science, mathematics or computing:

Film

Music

Geometry Dash

Geometry Dash is a 2013 mobile game and Steam game developed by Sweden-based developer Robert Topala, and published by his own company RobTop Games. It is a rhythm-based running game which currently has 20 levels. Each level features unique background music. Although the player is not required to complete a level to advance to the next, they increase in difficulty for the most part. Other features of the game that exist in the latest versions are a level editor, map packs, user-created levels, secret coins, user coins, a secret vault and a great variety of icons and game modes.

Gameplay

Geometry Dash uses a simple tapping/clicking system to control different vehicles that react when a player presses anywhere on the touchscreen (space/up key(s) or mouse if playing on the Steam version) and can be held down to constantly interact (on some vehicles). Users cannot control the speed at which the icon is moving, unless it interacts with a speed changing portal. The timing and rhythm are key parts of the game.

Geometry

Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of formal mathematical science emerging in the West as early as Thales (6th century BC). By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. In the classical world, both geometry and astronomy were considered to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.

Film festival

A film festival is an organized, extended presentation of films in one or more cinemas or screening venues, usually in a single city or region. Increasingly, film festivals show some films outdoors. Films may be of recent date and, depending upon the festival's focus, can include international and domestic releases. Some festivals focus on a specific film-maker or genre (e.g., film noir) or subject matter (e.g., horror film festivals). A number of film festivals specialise in short films of a defined maximum length. Film festivals are typically annual events. Some film historians do not consider Film Festivals as official releases of film, like Jerry Beck. The best known film festivals are the Venice Film Festival, the Cannes Film Festival, the Toronto Film Festival, Sundance Film Festival, and the Berlin International Film Festival, the latter being the largest film festival worldwide, based on attendance. The Venice Film Festival is the oldest major festival. The Melbourne International Film Festival is the largest film festival in the Southern Hemisphere and one of the oldest in the world. A 2013 study found 3,000 active films festivals worldwide—active defined as having held an event in the previous 24 months.