Analytic geometryIn mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions.
Magnetic pressureIn physics, magnetic pressure is an energy density associated with a magnetic field. In SI units, the energy density of a magnetic field with strength can be expressed as where is the vacuum permeability. Any magnetic field has an associated magnetic pressure contained by the boundary conditions on the field. It is identical to any other physical pressure except that it is carried by the magnetic field rather than (in the case of a gas) by the kinetic energy of gas molecules.
Algebraic geometryAlgebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations.
Taxicab geometryA taxicab geometry or a Manhattan geometry is a geometry whose usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian coordinates. The taxicab metric is also known as rectilinear distance, L1 distance, L1 distance or norm (see Lp space), snake distance, city block distance, Manhattan distance or Manhattan length.
Electromagnetic coilAn electromagnetic coil is an electrical conductor such as a wire in the shape of a coil (spiral or helix). Electromagnetic coils are used in electrical engineering, in applications where electric currents interact with magnetic fields, in devices such as electric motors, generators, inductors, electromagnets, transformers, and sensor coils. Either an electric current is passed through the wire of the coil to generate a magnetic field, or conversely, an external time-varying magnetic field through the interior of the coil generates an EMF (voltage) in the conductor.
Tesla coilA Tesla coil is an electrical resonant transformer circuit designed by inventor Nikola Tesla in 1891. It is used to produce high-voltage, low-current, high-frequency alternating-current electricity. Tesla experimented with a number of different configurations consisting of two, or sometimes three, coupled resonant electric circuits. Tesla used these circuits to conduct innovative experiments in electrical lighting, phosphorescence, X-ray generation, high-frequency alternating current phenomena, electrotherapy, and the transmission of electrical energy without wires.
Field-reversed configurationA field-reversed configuration (FRC) is a type of plasma device studied as a means of producing nuclear fusion. It confines a plasma on closed magnetic field lines without a central penetration. In an FRC, the plasma has the form of a self-stable torus, similar to a smoke ring. FRCs are closely related to another self-stable magnetic confinement fusion device, the spheromak. Both are considered part of the compact toroid class of fusion devices.
Congruence (geometry)In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object.
Electromagnetic fieldAn electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by moving electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified as light) and interacts with charges and currents.
Technological applications of superconductivityTechnological applications of superconductivity include: the production of sensitive magnetometers based on SQUIDs (superconducting quantum interference devices) fast digital circuits (including those based on Josephson junctions and rapid single flux quantum technology), powerful superconducting electromagnets used in maglev trains, magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) machines, magnetic confinement fusion reactors (e.g.
