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109 relations: Affine transformation, Alpha particle, Angle trisection, Apollonius of Perga, Area, Asymptote, Atomic nucleus, Bijection, Bow and arrow, Cartesian coordinate system, Celestial sphere, Circle, Comet, Concurrent lines, Cone, Conformal map, Congruence (geometry), Conic section, Connected component (graph theory), Coulomb's law, Cylinder, Dandelin spheres, Degenerate conic, Determinant, Director circle, Doubling the cube, Eccentricity (mathematics), Ellipse, Elliptic coordinate system, Envelope (mathematics), Escape velocity, Euclidean geometry, Focus (geometry), Geiger–Marsden experiment, Global Positioning System, Gold, Gravity assist, Greek language, Gyrovector space, Hesse normal form, Hyperbole, Hyperbolic function, Hyperbolic geometry, Hyperbolic growth, Hyperbolic navigation, Hyperbolic partial differential equation, Hyperbolic sector, Hyperbolic trajectory, Hyperboloid, Implicit function, ..., Inscribed angle, Inverse curve, Inverse function, Inverse-square law, Kepler problem, Korteweg–de Vries equation, Lemniscate of Bernoulli, Limaçon, Locus (mathematics), LORAN, Mathematical object, Mathematics, Matrix (mathematics), Menaechmus, Multilateration, Mutual fund separation theorem, Nikolai Lobachevsky, Non-Euclidean geometry, Normal (geometry), Orbit, Orthoptic (geometry), Osculating circle, Pappus of Alexandria, Parabola, Paraboloid, Pascal's theorem, Pencil (mathematics), Plane (geometry), Plane curve, Pole and polar, Principal branch, Projection (mathematics), Quadrant (plane geometry), Quadratic equation, Quadric, Quantum mechanics, Radius of curvature, Reflection (mathematics), Rotation (mathematics), Rotation matrix, Rotation of axes, Rutherford scattering, Similarity (geometry), Smoothness, Spacecraft, Springer Science+Business Media, Steiner conic, Strophoid, Subatomic particle, Sundial, Symmetry, Symmetry (geometry), Theory of relativity, Translation (geometry), Translation of axes, Triangle inequality, Trigonometric functions, Unit hyperbola, Zero of a function. Expand index (59 more) »
Affine transformation
In geometry, an affine transformation, affine mapBerger, Marcel (1987), p. 38.
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Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus.
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Angle trisection
Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.
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Apollonius of Perga
Apollonius of Perga (Ἀπολλώνιος ὁ Περγαῖος; Apollonius Pergaeus; late 3rdearly 2nd centuries BC) was a Greek geometer and astronomer known for his theories on the topic of conic sections.
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Area
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.
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Asymptote
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.
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Atomic nucleus
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Bow and arrow
The bow and arrow is a ranged weapon system consisting of an elastic launching device (bow) and long-shafted projectiles (arrows).
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Celestial sphere
In astronomy and navigation, the celestial sphere is an abstract sphere with an arbitrarily large radius concentric to Earth.
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Circle
A circle is a simple closed shape.
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Comet
A comet is an icy small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process called outgassing.
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Concurrent lines
In geometry, three or more lines in a plane or higher-dimensional space are said to be concurrent if they intersect at a single point.
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Cone
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
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Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
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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 mirror image of the other.
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Conic section
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.
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Connected component (graph theory)
In graph theory, a connected component (or just component) of an undirected graph is a subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices in the supergraph.
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Coulomb's law
Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other.
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Cylinder
A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.
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Dandelin spheres
In geometry, the Dandelin spheres are one or two spheres that are tangent both to a plane and to a cone that intersects the plane.
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Degenerate conic
In geometry, a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Director circle
In geometry, the director circle of an ellipse or hyperbola (also called the orthoptic circle or Fermat–Apollonius circle) is a circle consisting of all points where two perpendicular tangent lines to the ellipse or hyperbola cross each other.
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Doubling the cube
Doubling the cube, also known as the Delian problem, is an ancient geometric problem.
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Eccentricity (mathematics)
In mathematics, the eccentricity, denoted e or \varepsilon, is a parameter associated with every conic section.
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Ellipse
In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.
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Elliptic coordinate system
In geometry, the elliptic(al) coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae.
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Envelope (mathematics)
In geometry, an envelope of a family of curves in the plane is a curve that is tangent to each member of the family at some point, and these points of tangency together form the whole envelope.
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Escape velocity
In physics, escape velocity is the minimum speed needed for an object to escape from the gravitational influence of a massive body.
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Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
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Focus (geometry)
In geometry, focuses or foci, singular focus, are special points with reference to which any of a variety of curves is constructed.
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Geiger–Marsden experiment
The Geiger–Marsden experiment(s) (also called the Rutherford gold foil experiment) were a landmark series of experiments by which scientists discovered that every atom contains a nucleus where all of its positive charge and most of its mass are concentrated.
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Global Positioning System
The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Air Force.
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Gold
Gold is a chemical element with symbol Au (from aurum) and atomic number 79, making it one of the higher atomic number elements that occur naturally.
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Gravity assist
In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the path and speed of a spacecraft, typically to save propellant and reduce expense.
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Greek language
Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.
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Gyrovector space
A gyrovector space is a mathematical concept proposed by Abraham A. Ungar for studying hyperbolic geometry in analogy to the way vector spaces are used in Euclidean geometry.
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Hesse normal form
The Hesse normal form named after Otto Hesse, is an equation used in analytic geometry, and describes a line in \mathbb^2 or a plane in Euclidean space \mathbb^3 or a hyperplane in higher dimensions.
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Hyperbole
Hyperbole (ὑπερβολή, huperbolḗ, from ὑπέρ (hupér, "above") and βάλλω (bállō, "I throw")) is the use of exaggeration as a rhetorical device or figure of speech.
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Hyperbolic function
In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
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Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
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Hyperbolic growth
When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth.
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Hyperbolic navigation
Hyperbolic navigation refers to a class of navigation systems based on the difference in timing between the reception of two signals, without reference to a common clock.
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Hyperbolic partial differential equation
In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives.
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Hyperbolic sector
A hyperbolic sector is a region of the Cartesian plane bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the rectangular hyperbola xy.
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Hyperbolic trajectory
In astrodynamics or celestial mechanics, a hyperbolic trajectory is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull.
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Hyperboloid
In geometry, a hyperboloid of revolution, sometimes called circular hyperboloid, is a surface that may be generated by rotating a hyperbola around one of its principal axes.
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Implicit function
In mathematics, an implicit equation is a relation of the form R(x_1,\ldots, x_n).
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Inscribed angle
In geometry, an inscribed angle is the angle formed in the interior of a circle when two secant lines (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle.
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Inverse curve
In inversive geometry, an inverse curve of a given curve is the result of applying an inverse operation to.
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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Inverse-square law
The inverse-square law, in physics, is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity.
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Kepler problem
In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force F that varies in strength as the inverse square of the distance r between them.
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Korteweg–de Vries equation
In mathematics, the Korteweg–de Vries equation (KdV equation for short) is a mathematical model of waves on shallow water surfaces.
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Lemniscate of Bernoulli
In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2a from each other as the locus of points P so that PF1·PF2.
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Limaçon
In geometry, a limaçon or limacon, also known as a limaçon of Pascal, is defined as a roulette formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius.
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Locus (mathematics)
In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
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LORAN
LORAN, short for long range navigation, was a hyperbolic radio navigation system developed in the United States during World War II.
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Mathematical object
A mathematical object is an abstract object arising in mathematics.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Menaechmus
Menaechmus (Μέναιχμος, 380–320 BC) was an ancient Greek mathematician and geometer born in Alopeconnesus in the Thracian Chersonese, who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube using the parabola and hyperbola.
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Multilateration
Multilateration (MLAT) is a surveillance technique based on the measurement of the difference in distance to two stations at known locations by broadcast signals at known times.
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Mutual fund separation theorem
In portfolio theory, a mutual fund separation theorem, mutual fund theorem, or separation theorem is a theorem stating that, under certain conditions, any investor's optimal portfolio can be constructed by holding each of certain mutual funds in appropriate ratios, where the number of mutual funds is smaller than the number of individual assets in the portfolio.
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Nikolai Lobachevsky
Nikolai Ivanovich Lobachevsky (a; –) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry and also his fundamental study on Dirichlet integrals known as Lobachevsky integral formula.
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Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
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Normal (geometry)
In geometry, a normal is an object such as a line or vector that is perpendicular to a given object.
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Orbit
In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet.
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Orthoptic (geometry)
In the geometry of curves, an orthoptic is the set of points for which two tangents of a given curve meet at a right angle.
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Osculating circle
In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p and a pair of additional points on the curve infinitesimally close to p. Its center lies on the inner normal line, and its curvature is the same as that of the given curve at that point.
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Pappus of Alexandria
Pappus of Alexandria (Πάππος ὁ Ἀλεξανδρεύς; c. 290 – c. 350 AD) was one of the last great Greek mathematicians of Antiquity, known for his Synagoge (Συναγωγή) or Collection (c. 340), and for Pappus's hexagon theorem in projective geometry.
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Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
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Paraboloid
In geometry, a paraboloid is a quadric surface that has (exactly) one axis of symmetry and no center of symmetry.
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Pascal's theorem
In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem) states that if six arbitrary points are chosen on a conic (i.e., ellipse, parabola or hyperbola) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet in three points which lie on a straight line, called the Pascal line of the hexagon.
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Pencil (mathematics)
In projective geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a projective plane.
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Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
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Plane curve
In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane.
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Pole and polar
In geometry, the pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given conic section.
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Principal branch
In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function.
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Projection (mathematics)
In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent).
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Quadrant (plane geometry)
The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes.
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Quadratic equation
In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.
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Quadric
In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Radius of curvature
In differential geometry, the radius of curvature,, is the reciprocal of the curvature.
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Reflection (mathematics)
In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.
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Rotation (mathematics)
Rotation in mathematics is a concept originating in geometry.
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Rotation matrix
In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space.
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Rotation of axes
In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the origin is kept fixed and the x' and y' axes are obtained by rotating the x and y axes counterclockwise through an angle \theta.
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Rutherford scattering
Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction.
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Similarity (geometry)
Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Spacecraft
A spacecraft is a vehicle or machine designed to fly in outer space.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Steiner conic
The Steiner conic or more precisely Steiner's generation of a conic, named after the Swiss mathematician Jakob Steiner, is an alternative method to define a non-degenerate projective conic section in a projective plane over a field.
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Strophoid
In geometry, a strophoid is a curve generated from a given curve C and points A (the fixed point) and O (the pole) as follows: Let L be a variable line passing through O and intersecting C at K. Now let P1 and P2 be the two points on L whose distance from K is the same as the distance from A to K. The locus of such points P1 and P2 is then the strophoid of C with respect to the pole O and fixed point A. Note that AP1 and AP2 are at right angles in this construction.
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Subatomic particle
In the physical sciences, subatomic particles are particles much smaller than atoms.
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Sundial
A sundial is a device that tells the time of day when there is sunlight by the apparent position of the Sun in the sky.
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Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.
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Symmetry (geometry)
A geometric object has symmetry if there is an "operation" or "transformation" (such as an isometry or affine map) that maps the figure/object onto itself; i.e., it is said that the object has an invariance under the transform.
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Theory of relativity
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity.
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Translation (geometry)
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction.
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Translation of axes
In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away.
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Triangle inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
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Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
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Unit hyperbola
In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation x^2 - y^2.
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Zero of a function
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).
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Conjugate hyperbola, Equilateral hyperbola, Hiperbola, Hyperbola (mathematics), Hyperbolae, Hyperbolas, Hyperbolic arc, Rectangular hyperbola, Right hyperbola.
References
[1] https://en.wikipedia.org/wiki/Hyperbola
