Square root of 2

The square root of 2, written in mathematics as √2 or 2^1⁄₂, is the positive algebraic number that, when multiplied by itself, gives the number 2. Technically, it is called the principal square root of 2, to distinguish it from the negative number with the same property.

Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. Its numerical value, truncated to 65 decimal places, is:

The approximation 99/70 (≈ 1.41429) for the square root of two is frequently used. Despite having a denominator of only 70, it differs from the correct value by less than 1/10,000 (approx. 6995720000000000000♠7.2×10⁻⁵). The approximation 665,857/470,832 is valid to within 6988112999999999999♠1.13×10⁻¹²: its square is 7000200000000000450♠2.0000000000045….

History

The Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) gives an approximation of √2 in four sexagesimal figures, 1 24 51 10, which is accurate to about six decimal digits, and is the closest possible three-place sexagesimal representation of √2:

War Thunder

War Thunder is a World War II-inspired massively multiplayer online combat game developed by Gaijin Entertainment for Microsoft Windows, OS X, Linux, PlayStation 4 and Shield Android TV.

Game model

The game is modeled on a micro-transaction system but with the ability to get almost every feature of the game without paying. This may require players to complete certain challenges (such as shooting down a certain number of enemy aircraft or destroying a certain number of ground targets), or submitting user created content such as skins, or camouflage for vehicles. There may also be other celebratory events throughout the year such as commemorating historic figures in aviation or famous battles allowing players to win premium currency and premium vehicles without any expenditure.

There is also a referral service, whereby players can invite people to the game, earning both themselves and the new player an in-game bonus.

Game Currency

War Thunder uses 4 main currencies: Silver Lions, Golden Eagles, Research Points, and Convertible Research Points.

Battlefield 4

Battlefield 4 is a 2013 first-person shooter video game developed by Swedish video game developer EA Digital Illusions CE (DICE) and published by Electronic Arts. It is a sequel to 2011's Battlefield 3 and was released on October 29, 2013 in North America, October 31, 2013 in Australia, November 1, 2013 in Europe and New Zealand and November 7, 2013 in Japan for Microsoft Windows, PlayStation 3, PlayStation 4, Xbox 360 and Xbox One.

Battlefield 4 was met with positive reception. It was praised for its multiplayer mode, gameplay and graphics, but was also criticized for its short and shallow single-player campaign mode, and for its numerous bugs and glitches. It was a commercial success, selling over 7 million copies.

Gameplay

The game's heads-up display (HUD) is composed of two compact rectangles. The lower left-hand corner features a mini-map and compass for navigation, and a simplified objective notice above it; the lower right includes a compact ammo counter and health meter. The top right displays kill notifications of all players in-game. On the Windows version of the game, the top left features a chat window when in multiplayer. The mini-map, as well as the main game screen, shows symbols marking three kinds of entities: blue for allies, green for squadmates, and orange for enemies, this applies to all interactivity on the battlefield. Battlefield 4 options also allow colour-blind players to change the on-screen colour indicators to: tritanomaly, deuteranomaly and protanomaly.

PlanetSide 2

PlanetSide 2 is a free-to-play massively multiplayer online first-person shooter published by Daybreak Game Company and released on November 20, 2012. It is a sequel of PlanetSide which originally was released in 2003. Officially announced on July 7, 2011 at the Sony Fan Fair, the second installment used a new game engine, supported thousands of players in continuous large scale conflict, and featured in-game integration with Twitch.tv. As in the first PlanetSide, PlanetSide 2 chronicles the efforts of three factions as they fight for territorial control of the planet Auraxis.PlanetSide 2 was released for the PlayStation 4 in North America on June 23, 2015.PlanetSide 2 holds the Guinness World Record for the biggest first-person shooter battle with 1158 players in a single battle.

Gameplay

PlanetSide 2 is a re-imagining of PlanetSide, featuring the same world and factions, and taking place at roughly the same time period. As in the previous game, it features territory control in an open-world, large battles featuring up to 2000 players per continent on foot or in land/air vehicles. The territory system differs greatly from that of the original, being more free-form and based on a hexagonal territory control system. Former SOE (now DGC) has been taking into account balance issues from the first game. As stated by creative director Matthew Higby, they reward combatants on lower population empires through mechanics such as proportionally increased advancement rates and resources to aid the balance of overall empire saturation on each server as much as possible without force-restricting players from being able to play with their friends.