Pentagon

In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°.

A pentagon may be simple or self-intersecting. A self-intersecting regular pentagon (or star pentagon) is called a pentagram.

Regular pentagons

A regular pentagon has Schläfli symbol {5} and interior angles are 108°.

A regular pentagon has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72°, 144°, 216° and 288°). The diagonals of a convex regular pentagon are in the golden ratio to its sides. Its height (distance from one side to the opposite vertex) and width (distance between two farthest separated points, which equals the diagonal length) are given by

where R is the radius of the circumcircle.

The area of a convex regular convex pentagon with side length t is given by

A pentagram or pentangle is a regular star pentagon. Its Schläfli symbol is {5/2}. Its sides form the diagonals of a regular convex pentagon – in this arrangement the sides of the two pentagons are in the golden ratio.

Subtitle (captioning)

Subtitles are derived from either a transcript or screenplay of the dialog or commentary in films, television programs, video games, and the like, usually displayed at the bottom of the screen, but can also be at the top of the screen if there is already text at the bottom of the screen. They can either be a form of written translation of a dialog in a foreign language, or a written rendering of the dialog in the same language, with or without added information to help viewers who are deaf and hard of hearing to follow the dialog, or people who cannot understand the spoken dialogue or who have accent recognition problems. The encoded method can either be pre-rendered with the video or separate as either a graphic or text to be rendered and overlaid by the receiver. The separate subtitles are used for DVD, Blu-ray and television teletext/Digital Video Broadcasting (DVB) subtitling or EIA-608 captioning, which are hidden unless requested by the viewer from a menu or remote controller key or by selecting the relevant page or service (e.g., p. 888 or CC1), always carry additional sound representations for deaf and hard of hearing viewers. Teletext subtitle language follows the original audio, except in multi-lingual countries where the broadcaster may provide subtitles in additional languages on other teletext pages. EIA-608 captions are similar, except that North American Spanish stations may provide captioning in Spanish on CC3. DVD and Blu-ray only differ in using run-length encoded graphics instead of text, as well as some HD DVB broadcasts.

Official

An official is someone who holds an office (function or mandate, regardless whether it carries an actual working space with it) in an organization or government and participates in the exercise of authority (either his own or that of his superior and/or employer, public or legally private).

A government official or functionary is an official who is involved in public administration or government, through either election, appointment, selection, or employment. A bureaucrat or civil servant is a member of the bureaucracy. An elected official is a person who is an official by virtue of an election. Officials may also be appointed ex officio (by virtue of another office, often in a specified capacity, such as presiding, advisory, secretary). Some official positions may be inherited. A person who currently holds an office is referred to as an incumbent.

The word official as a noun has been recorded since the Middle English period, first seen in 1314. It comes from the Old French official (12th century), from the Latin officialis ("attendant to a magistrate, public official"), the noun use of the original adjective officialis ("of or belonging to duty, service, or office") from officium ("office"). The meaning "person in charge of some public work or duty" was first recorded in 1555. The adjective is first attested in English in 1533, via the Old French oficial.

After School Club

After School Club, often shortened to ASC, is a South Korean internet based live music request television talk show hosted by K-pop idol Eric Nam and co-hosted by Kevin Woo and Park Jimin. Debuting on April 17, 2013, it is produced by Park Jeong-Wo and airs on Arirang TV. ASC features various musical guests of South Korea and the series is directed at an international audience so the principal language is English with Korean subtitles and translations produced on air. It allows international fans of K-pop music to interact directly with the live shows through social media. Fans can join in on the live broadcasts through video chats in Google Hangout, send in tweets to the show's official Twitter Account. Fans are also able to share comments on the show's official Facebook account and ask questions and request their favourite music videos. The show is also available on Viki (website), a community for subtitles and on Soompi.

Premise and format

The show broadcasts live online and utilizes social media technologies such as Twitter and Google Hangout to directly interact with international fans. Two activities that take place every episode are the Roll Calls and Hangouts. During the Roll Call portion Twitter users tweet their name, location, the time and generally a short message to the weekly guest. Those that participate may be singled out during the beginning of the episode and given a shout out by the guest. "Hangouts" are typically done twice an episode where some fans are selected for a real-time Google Hangout on the show which usually involves something (such as a song or dance) prepared by the fan to show to the guest(s) and a request. Other activities include prepared performances for fans by the guests, such as impressions, dances, and short parodies.

After School

After School may refer to:

Films

Music