Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with a room's walls extended infinitely far, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry.

When working exclusively in two-dimensional Euclidean space, the definite article is used, so, the plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory and graphing are performed in a two-dimensional space, or in other words, in the plane.

Euclidean geometry

Euclid set forth the first great landmark of mathematical thought, an axiomatic treatment of geometry. He selected a small core of undefined terms (called common notions) and postulates (or axioms) which he then used to prove various geometrical statements. Although the plane in its modern sense is not directly given a definition anywhere in the Elements, it may be thought of as part of the common notions. In his work Euclid never makes use of numbers to measure length, angle, or area. In this way the Euclidean plane is not quite the same as the Cartesian plane.

Flat Earth

The flat Earth model is an archaic conception of the Earth's shape as a plane or disk. Many ancient cultures subscribed to a flat Earth cosmography, including Greece until the classical period, the Bronze Age and Iron Age civilizations of the Near East until the Hellenistic period, India until the Gupta period (early centuries AD) and China until the 17th century. That paradigm was also typically held in the aboriginal cultures of the Americas, and the notion of a flat Earth domed by the firmament in the shape of an inverted bowl was common in pre-scientific societies.

The idea of a spherical Earth appeared in Greek philosophy with Pythagoras (6th century BC), although most Pre-Socratics retained the flat Earth model. Aristotle accepted the spherical shape of the Earth on empirical grounds around 330 BC, and knowledge of the spherical Earth gradually began to spread beyond the Hellenistic world from then on.

Historical development

Ancient Near East

In early Egyptian and Mesopotamian thought the world was portrayed as a flat disk floating in the ocean. A similar model is found in the Homeric account of the 8th century BC in which "Okeanos, the personified body of water surrounding the circular surface of the Earth, is the begetter of all life and possibly of all gods." The Israelites likely had a similar cosmology, with the earth as a flat disc floating on water beneath an arced firmament separating it from the heavens.

Flat

flat commonly refers to:

Flat or flats may also refer to:

Geography

Places

Landforms

Architecture

Earth

Earth /ˈɜːrθ/ (also the world, in Greek: Γαῖα Gaia, or in Latin: Terra) is the third planet from the Sun, the densest planet in the Solar System, the largest of the Solar System's four terrestrial planets, and the only astronomical object known to harbor life.

According to evidence from radiometric dating and other sources, Earth was formed about 4.54 billion years ago. Earth gravitationally interacts with other objects in space, especially the Sun and the Moon. During one orbit around the Sun, Earth rotates about its own axis 366.26 times, creating 365.26 solar days or one sidereal year. Earth's axis of rotation is tilted 23.4° away from the perpendicular of its orbital plane, producing seasonal variations on the planet's surface with a period of one tropical year (365.24 solar days). The Moon is Earth's only permanent natural satellite. Its gravitational interaction with Earth causes ocean tides, stabilizes the orientation of Earth's rotational axis, and gradually slows Earth's rotational rate.

A Flat (film)

A Flat is a Hindi thriller film, directed by Hemant Madhukar and produced by Anjum Rizvi.The film was released on 12 November 2010 under the Anjum Rizvi Film Company and Y.T Entertainment Ltd. banners.

Plot

The story follows Rahul (Jimmy Shergill), a young businessman who comes back from the U.S. to patch things up with his girlfriend Preeti (Kaveri Jha). His father, Varma (Sachin Khedekar) is mysteriously murdered as he goes to find a flat for Rahul. His friend Karan (Sanjay Suri), a rich salesman, gives his old flat to Rahul. After Rahul enters the flat, his life takes an unexpected turn when the unexplainable disappearance of Preeti takes place, and finally Rahul finds himself trapped in his own flat. With no connection to the outside world, Rahul is stuck and realises that a ghost is living in the flat with him, who won't let him go. He tries to contact Karan, but is unsuccessful. He then finds a diary in his room, which is opened by the ghost who allows him to read it.

It turns out the diary belongs to Geethika (Hazel Crowney), a young village girl living out her childhood even at an adult age. She finds Karan coming to her village to build many buildings, and Karan uses Geethika's father's help. When her father cancells it of due to the suicide of her sister, Karan can't take the loss, and runs away with Geethika pretending to be in love with her. Back in a flashback, it is shown the two coming to foreign and getting married in the same flat Rahul is living in. Karan explains that he will return in a few days, but doesn't come back until many months. In his absence, Varma visits Geethika and takes advantage and tries to rape her. She uses self-defence, and tells him to get out. She begins to cry, only to realise she is pregnant. Karan comes back, and tells her to abort the baby because he is already married to someone else. She dies during the abortion, and Karan hides her body so nobody would blame him for her death.