Projective geometryIn mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "points at infinity") to Euclidean points, and vice-versa.
Symmetry (geometry)In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). Thus, a symmetry can be thought of as an immunity to change. For instance, a circle rotated about its center will have the same shape and size as the original circle, as all points before and after the transform would be indistinguishable.
Synthetic geometrySynthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulate, and at present called axioms. The term "synthetic geometry" has been coined only after the 17th century, and the introduction by René Descartes of the coordinate method, which was called analytic geometry.
Icosahedral symmetryIn mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other polyhedra with icosahedral symmetry include the regular dodecahedron (the dual of the icosahedron) and the rhombic triacontahedron. Every polyhedron with icosahedral symmetry has 60 rotational (or orientation-preserving) symmetries and 60 orientation-reversing symmetries (that combine a rotation and a reflection), for a total symmetry order of 120.
Orthographic map projectionOrthographic projection in cartography has been used since antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or azimuthal) projection in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic projection is at infinite distance. It depicts a hemisphere of the globe as it appears from outer space, where the horizon is a great circle. The shapes and areas are distorted, particularly near the edges.
Absolute geometryAbsolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally, this has meant using only the first four of Euclid's postulates. The term was introduced by János Bolyai in 1832. It is sometimes referred to as neutral geometry, as it is neutral with respect to the parallel postulate. The first four of Euclid's postulates are now considered insufficient as a basis of Euclidean geometry, so other systems (such as Hilbert's axioms without the parallel axiom) are used instead.
Window (computing)In computing, a window is a graphical control element. It consists of a visual area containing some of the graphical user interface of the program it belongs to and is framed by a window decoration. It usually has a rectangular shape that can overlap with the area of other windows. It displays the output of and may allow input to one or more processes. Windows are primarily associated with graphical displays, where they can be manipulated with a pointer by employing some kind of pointing device.
Window managerA window manager is system software that controls the placement and appearance of windows within a windowing system in a graphical user interface. Most window managers are designed to help provide a desktop environment. They work in conjunction with the underlying graphical system that provides required functionality—support for graphics hardware, pointing devices, and a keyboard—and are often written and created using a widget toolkit. Few window managers are designed with a clear distinction between the windowing system and the window manager.
Home constructionHome construction or residential construction is the process of constructing a house, apartment building, or similar residential building generally referred to as a 'home' when giving consideration to the people who might now or someday reside there. Beginning with simple pre-historic shelters, home construction techniques have evolved to produce the vast multitude of living accommodations available today. Different levels of wealth and power have warranted various sizes, luxuries, and even defenses in a "home".
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
Steiner ellipseIn geometry, the Steiner ellipse of a triangle, also called the Steiner circumellipse to distinguish it from the Steiner inellipse, is the unique circumellipse (ellipse that touches the triangle at its vertices) whose center is the triangle's centroid. Named after Jakob Steiner, it is an example of a circumconic. By comparison the circumcircle of a triangle is another circumconic that touches the triangle at its vertices, but is not centered at the triangle's centroid unless the triangle is equilateral.
Tiling window managerIn computing, a tiling window manager is a window manager with an organization of the screen into mutually non-overlapping frames, as opposed to the more common approach (used by stacking window managers) of coordinate-based stacking of overlapping objects (windows) that tries to fully emulate the desktop metaphor. The first Xerox Star system (released in 1981) tiled application windows, but allowed dialogs and property windows to overlap. Later, Xerox PARC also developed CEDAR (released in 1982), the first windowing system using a tiled window manager.
