SymmetrySymmetry () in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
Augmented realityAugmented reality (AR) is an interactive experience that combines the real world and computer-generated content. The content can span multiple sensory modalities, including visual, auditory, haptic, somatosensory and olfactory. AR can be defined as a system that incorporates three basic features: a combination of real and virtual worlds, real-time interaction, and accurate 3D registration of virtual and real objects. The overlaid sensory information can be constructive (i.e. additive to the natural environment), or destructive (i.
Symmetry groupIn group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object X is G = Sym(X). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space.
Rotational symmetryRotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids.
Electronic paperElectronic paper, also known as electronic ink (e-ink) or intelligent paper, is a display device that mimics the appearance of ordinary ink on paper. Unlike conventional flat panel displays that emit light, an electronic paper display reflects ambient light, like paper. This may make them more comfortable to read, and provide a wider viewing angle than most light-emitting displays. The contrast ratio in electronic displays available as of 2008 approaches newspaper, and newly developed displays are slightly better.
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.
Circular symmetryIn geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the special orthogonal group SO(2), and unitary group U(1). Reflective circular symmetry is isomorphic with the orthogonal group O(2). A 2-dimensional object with circular symmetry would consist of concentric circles and annular domains.
Reflection symmetryIn mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called . In conclusion, a line of symmetry splits the shape in half and those halves should be identical.
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.
User interfaceIn the industrial design field of human–computer interaction, a user interface (UI) is the space where interactions between humans and machines occur. The goal of this interaction is to allow effective operation and control of the machine from the human end, while the machine simultaneously feeds back information that aids the operators' decision-making process. Examples of this broad concept of user interfaces include the interactive aspects of computer operating systems, hand tools, heavy machinery operator controls and process controls.
Paper prototypingIn human–computer interaction, paper prototyping is a widely used method in the user-centered design process, a process that helps developers to create software that meets the user's expectations and needs – in this case, especially for designing and testing user interfaces. It is throwaway prototyping and involves creating rough, even hand-sketched, drawings of an interface to use as prototypes, or models, of a design. While paper prototyping seems simple, this method of usability testing can provide useful feedback to aid the design of easier-to-use products.
Virtual realityVirtual reality (VR) is a simulated experience that employs pose tracking and 3D near-eye displays to give the user an immersive feel of a virtual world. Applications of virtual reality include entertainment (particularly video games), education (such as medical or military training) and business (such as virtual meetings). Other distinct types of VR-style technology include augmented reality and mixed reality, sometimes referred to as extended reality or XR, although definitions are currently changing due to the nascence of the industry.
Organic user interfaceIn human–computer interaction, an organic user interface (OUI) is defined as a user interface with a non-flat display. After Engelbart and Sutherland's graphical user interface (GUI), which was based on the cathode ray tube (CRT), and Kay and Weiser's ubiquitous computing, which is based on the flat panel liquid-crystal display (LCD), OUI represents one possible third wave of display interaction paradigms, pertaining to multi-shaped and flexible displays.
Human–computer interactionHuman–computer interaction (HCI) is research in the design and the use of computer technology, which focuses on the interfaces between people (users) and computers. HCI researchers observe the ways humans interact with computers and design technologies that allow humans to interact with computers in novel ways. A device that allows interaction between human being and a computer is known as a "Human-computer Interface (HCI)".
Symmetry in biologySymmetry in biology refers to the symmetry observed in organisms, including plants, animals, fungi, and bacteria. External symmetry can be easily seen by just looking at an organism. For example, the face of a human being has a plane of symmetry down its centre, or a pine cone displays a clear symmetrical spiral pattern. Internal features can also show symmetry, for example the tubes in the human body (responsible for transporting gases, nutrients, and waste products) which are cylindrical and have several planes of symmetry.
Tangible user interfaceA tangible user interface (TUI) is a user interface in which a person interacts with digital information through the physical environment. The initial name was Graspable User Interface, which is no longer used. The purpose of TUI development is to empower collaboration, learning, and design by giving physical forms to digital information, thus taking advantage of the human ability to grasp and manipulate physical objects and materials.
PaperPaper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, rags, grasses, or other vegetable sources in water, draining the water through a fine mesh leaving the fibre evenly distributed on the surface, followed by pressing and drying. Although paper was originally made in single sheets by hand, almost all is now made on large machines—some making reels 10 metres wide, running at 2,000 metres per minute and up to 600,000 tonnes a year.
Computer-mediated realityComputer-mediated reality refers to the ability to add to, subtract information from, or otherwise manipulate one's perception of reality through the use of a wearable computer or hand-held device such as a smartphone. Mediated reality is a proper superset of mixed reality, augmented reality, and virtual reality, as it also includes, for example, diminished reality. Typically, it is the user's visual perception of the environment that is mediated.
Modality (human–computer interaction)In the context of human–computer interaction, a modality is the classification of a single independent channel of input/output between a computer and a human. Such channels may differ based on sensory nature (e.g., visual vs. auditory), or other significant differences in processing (e.g., text vs. image). A system is designated unimodal if it has only one modality implemented, and multimodal if it has more than one. When multiple modalities are available for some tasks or aspects of a task, the system is said to have overlapping modalities.
Mobile interactionMobile interaction is the study of interaction between mobile users and computers. Mobile interaction is an aspect of human–computer interaction that emerged when computers became small enough to enable mobile usage, around the 1990s. Mobile devices are a pervasive part of people's everyday lives. People use mobile phones, PDAs, and portable media players almost everywhere. These devices are the first truly pervasive interaction devices that are currently used for a huge variety of services and applications.
