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.

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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.

United States Department of Defense

The Department of Defense (DoD,USDOD, or DOD) is an executive branch department of the federal government of the United States charged with coordinating and supervising all agencies and functions of the government concerned directly with national security and the United States Armed Forces. The Department is also the largest employer in the world, with more than 2.13 million active duty servicemen and women as well as their support staff of civilian workers. Adding to the total is over 1.1 million National Guardsmen and Reservists from the four services, bringing the total to just over 3.2 million employees. It is headquartered at the Pentagon in Arlington, Virginia, just outside of Washington D.C.

The Department of Defense is headed by the Secretary of Defense, a cabinet-level head who reports directly to the President of the United States. Beneath the Department of Defense are three subordinate military departments: the United States Department of the Army, the United States Department of the Navy, and the United States Department of the Air Force. In addition, four national intelligence services are subordinate to the Department of Defense: the Defense Intelligence Agency (DIA), the National Security Agency (NSA), the National Geospatial-Intelligence Agency (NGA), and the National Reconnaissance Office (NRO). Other Defense Agencies include the Defense Advanced Research Projects Agency (DARPA), the Defense Logistics Agency (DLA), the Missile Defense Agency (MDA), Defense Threat Reduction Agency (DTRA), and the Pentagon Force Protection Agency (PFPA), all of which are under the command of the Secretary of Defense. Military operations are managed by nine regional or functional Unified Combatant Commands. The Department of Defense also operates several joint services schools, including the National Defense University (NDU) and the National War College (NWC).

South Korea

Coordinates: 36°N 128°E / 36°N 128°E / 36; 128

South Korea ( listen), officially the Republic of Korea (Hangul: 대한민국; hanja: 大韓民國; RR: Daehanminguk,  listen) and commonly referred to as Korea, is a sovereign state in East Asia, constituting the southern part of the Korean Peninsula. The name Korea is derived from the ancient Kingdom of Goguryeo, also known as Koryŏ. Highly urbanized at 92%, Koreans lead a distinctive urban lifestyle with half of them living in the Seoul Capital Area, the world's second largest city with over 25 million residents and a leading global city with the fourth largest economy, rated in 2016 as the world's most livable megacity and safest city to live in. Highly mountainous, Korea is a popular winter sport destination in Asia, hosting the 2018 Winter Olympics.

The earliest Korean pottery dates to 8000 BC, with three kingdoms flourishing at 1st century BC. One of them, Goguryeo, ruled Northeast China, parts of Russia and Mongolia under Gwanggaeto the Great. Since their unification into Silla and Balhae in the 7th century, Korea enjoyed over a millennium of relative tranquility under long lasting dynasties with innovations like Hangul, the unique alphabet created by Sejong the Great in 1446, enabling anyone to easily learn to read and write. Its rich and vibrant culture left 17 UNESCO Intangible Cultural Heritages of Humanity, the third largest in the world, along with 12 World Heritage Sites. Korea was annexed by Imperial Japan in 1910 due to its strategic and central location, after whose surrender in 1945, it was divided into North and South Korea. A North Korean invasion lead to the Korean War (1950–53). Peace has since mostly continued with the two agreeing to work peacefully for reunification and the South solidifying peace as a regional power with the world's 10th largest defence budget and strong global alliances. In 2016, Korea was rated as the world's safest country to live in, with the lowest crime rate.