Two-dimensional space

In physics and mathematics, two-dimensional space or bi-dimensional space is a geometric model of the planar projection of the physical universe. The two dimensions are commonly called length and width. Both directions lie in the same plane.

A sequence of n real numbers can be understood as a location in n-dimensional space. When n = 2, the set of all such locations is called two-dimensional space or bi-dimensional space, and usually is thought of as a Euclidean space.

History

Books I through IV and VI of Euclid's Elements dealt with two-dimensional geometry, developing such notions as similarity of shapes, the Pythagorean theorem (Proposition 47), equality of angles and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are "equal" (have the same area), among many other topics.

Later, the plane was described in a so-called Cartesian coordinate system, a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.

Mathematical fallacy

In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the best-known examples of mathematical fallacies, there is some concealment in the presentation of the proof. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a striking quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way. Therefore, these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and should not be applied in the cases that are the exceptions to the rules.

XY

XY or Xy may refer to:

coordinates, a system used to locate a point in two dimensions according to the cartesian coordinate system

See also

Pokémon X and Y

Pokémon X and Pokémon Y (ポケットモンスター X・Y, Poketto Monsutā Ekkusu & Wai) are role-playing video games developed by Game Freak and published by Nintendo for the Nintendo 3DS. They are the first installments in the sixth generation of the Pokémon series of role-playing games. First announced on January 8, 2013, by Satoru Iwata through a special Nintendo Direct, both X and Y were released worldwide on October 12, 2013, making them the first Nintendo-published retail games to have such a global simultaneous release in all key regions.

As with previous installments, each game follows the journey of a young Pokémon trainer (and the trainer's friends) as they train Pokémon. This time, the game takes place in the Kalos region—based on France—with the object of the game being to thwart the schemes of the nefarious criminal organization Team Flare, all while attempting to challenge the Pokémon League Champion. X and Y introduced 70 new Pokémon species, and includes new features such as the new Fairy type, character customization, updated battle and training mechanics, and completely rendered polygonal 3D graphics (as opposed to the sprites used in previous generations). A new form of Pokémon evolution, known as "Mega Evolution," allows players to further evolve many species of fully evolved Pokémon, with 30 evolutions currently available. Both titles are independent of each other, but feature largely the same plot, and while either can be played separately, trading Pokémon between the two games is, as with past titles, necessary in order for a player to obtain every Pokémon species.