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Index Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. [1]

161 relations: Affine transformation, Aircraft, Algebra, Algebraic geometry, American Mathematical Monthly, Angle, Angle trisection, Apex (geometry), Apollonius of Perga, Arc (geometry), Archimedes, Ballistic missile, Bézier curve, Bisection, Bouncing ball, Canada, Cardioid, Cartesian coordinate system, Catenary, Center of mass, Centrifugal force, Chord (geometry), Collimated light, Comet, Comet Kohoutek, Compass-and-straightedge construction, Completing the square, Cone, Conic section, Conical surface, Coplanarity, Cramer's rule, Cross section (geometry), Curved mirror, Cut-the-Knot, Cylinder, Dandelin spheres, De Casteljau's algorithm, Definite quadratic form, Degeneracy (mathematics), Degenerate conic, Distance from a point to a line, Doubling the cube, Drag (physics), Eccentricity (mathematics), Electromagnetic radiation, Ellipse, Elliptic orbit, Engineering, Equidistant, ..., Escape velocity, Field (mathematics), Focus (geometry), Focus (optics), Free fall, Friction, Function composition, Galileo Galilei, Gaussian elimination, Graph of a function, Gravitational field, Hesse normal form, Hyperbola, Hyperbolic trajectory, Hyperboloid, Hypothesis, Implicit function, Inscribed angle, Intercept theorem, Intersecting chords theorem, Intersection (Euclidean geometry), Inversive geometry, Irreducible polynomial, Isaac Newton, Isosceles triangle, Jakob Steiner, James Gregory (mathematician), Johann Heinrich Lambert, Light, Line (geometry), Liquid mirror telescope, Locus (mathematics), Marin Mersenne, Mathematician, Mathematics, Menaechmus, Method of exhaustion, Microwave, NASA, Natural logarithm, Newton's reflector, Niagara River, Numerical integration, Pappus of Alexandria, Parabolic antenna, Parabolic microphone, Parabolic partial differential equation, Parabolic reflector, Parabolic trajectory, Parabolic trough, Paraboloid, Parallel (geometry), Parallelogram, Parametric equation, Pascal's theorem, Pedal curve, Pencil (mathematics), Physics, Plane (geometry), Plane curve, Point (geometry), Polar coordinate system, Pole and polar, Polynomial, Pythagorean theorem, Quadratic equation, Quadratic form, Quadratic function, Quadric, Radius of curvature, Rainbow Bridge (Niagara Falls), Rational normal curve, Reduced-gravity aircraft, Reflecting telescope, Reflection (physics), Reflection symmetry, René Descartes, Roman Empire, Rotating furnace, Rotation of axes, Rotational symmetry, Scaling (geometry), Shape, Similarity (geometry), Simpson's rule, Solar cooker, Solar energy, Sound, Springer Science+Business Media, Square root, Steiner conic, Stephen Hawking, Sun, Suspension bridge, Synthetic geometry, Syracuse, Sicily, Tangent, Telescope, The Quadrature of the Parabola, Thomas Edison, Trajectory, Translation of axes, Trisectrix, Twisted cubic, Two-body problem, United States, Universal parabolic constant, University of Texas at Austin, Veronese surface, Vertex (curve), Weightlessness. Expand index (111 more) »

Affine transformation

In geometry, an affine transformation, affine mapBerger, Marcel (1987), p. 38.

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An aircraft is a machine that is able to fly by gaining support from the air.

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Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

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Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

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American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

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In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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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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Apex (geometry)

In geometry, an apex (Latin for 'summit, peak, tip, top, extreme end') is the vertex which is in some sense the "highest" of the figure to which it belongs.

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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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Arc (geometry)

In Euclidean geometry, an arc (symbol: ⌒) is a closed segment of a differentiable curve.

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Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.

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Ballistic missile

A ballistic missile follows a ballistic trajectory to deliver one or more warheads on a predetermined target.

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Bézier curve

A Bézier curve (pronounced in French) is a parametric curve frequently used in computer graphics and related fields.

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In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.

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Bouncing ball

The physics of a bouncing ball concerns the physical behaviour of bouncing balls, particularly its motion before, during, and after impact against the surface of another body.

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Canada is a country located in the northern part of North America.

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A cardioid (from the Greek καρδία "heart") is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius.

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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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In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends.

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Center of mass

In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero, or the point where if a force is applied it moves in the direction of the force without rotating.

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Centrifugal force

In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) directed away from the axis of rotation that appears to act on all objects when viewed in a rotating frame of reference.

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Chord (geometry)

A chord of a circle is a straight line segment whose endpoints both lie on the circle.

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Collimated light

Collimated light is light whose rays are parallel, and therefore will spread minimally as it propagates.

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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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Comet Kohoutek

Comet Kohoutek, formally designated C/1973 E1, 1973 XII, and 1973f, was first sighted on 7 March 1973 by Czech astronomer Luboš Kohoutek.

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Compass-and-straightedge construction

Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.

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Completing the square

In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of h and k. Completing the square is used in.

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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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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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Conical surface

In geometry, a (general) conical surface is the unbounded surface formed by the union of all the straight lines that pass through a fixed point — the apex or vertex — and any point of some fixed space curve — the directrix — that does not contain the apex.

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In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all.

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Cramer's rule

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.

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Cross section (geometry)

In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces.

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Curved mirror

A curved mirror is a mirror with a curved reflecting surface.

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Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.

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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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De Casteljau's algorithm

In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau.

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Definite quadratic form

In mathematics, a definite quadratic form is a quadratic form over some real vector space that has the same sign (always positive or always negative) for every nonzero vector of.

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Degeneracy (mathematics)

In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class.

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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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Distance from a point to a line

The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry.

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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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Drag (physics)

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.

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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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Electromagnetic radiation

In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space-time, carrying electromagnetic radiant energy.

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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 orbit

In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0.

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Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.

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A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

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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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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

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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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Focus (optics)

In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge.

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Free fall

In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it.

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Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.

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Function composition

In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.

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Galileo Galilei

Galileo Galilei (15 February 1564Drake (1978, p. 1). The date of Galileo's birth is given according to the Julian calendar, which was then in force throughout Christendom. In 1582 it was replaced in Italy and several other Catholic countries with the Gregorian calendar. Unless otherwise indicated, dates in this article are given according to the Gregorian calendar. – 8 January 1642) was an Italian polymath.

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Gaussian elimination

In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.

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Graph of a function

In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

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Gravitational field

In physics, a gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body.

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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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In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

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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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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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A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon.

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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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Intercept theorem

The intercept theorem, also known as Thales' theorem (not to be confused with another theorem with that name) or basic proportionality theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels.

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Intersecting chords theorem

The intersecting chords theorem or just chord theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords in a circle.

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Intersection (Euclidean geometry)

In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces).

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Inversive geometry

In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion.

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Irreducible polynomial

In mathematics, an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials.

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Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

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Isosceles triangle

In geometry, an isosceles triangle is a triangle that has two sides of equal length.

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Jakob Steiner

Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry.

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James Gregory (mathematician)

James Gregory FRS (November 1638 – October 1675) was a Scottish mathematician and astronomer.

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Johann Heinrich Lambert

Johann Heinrich Lambert (Jean-Henri Lambert in French; 26 August 1728 – 25 September 1777) was a Swiss polymath who made important contributions to the subjects of mathematics, physics (particularly optics), philosophy, astronomy and map projections.

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Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum.

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Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

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Liquid mirror telescope

Liquid mirror telescopes are telescopes with mirrors made with a reflective liquid.

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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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Marin Mersenne

Marin Mersenne, Marin Mersennus or le Père Mersenne (8 September 1588 – 1 September 1648) was a French polymath, whose works touched a wide variety of fields.

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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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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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Method of exhaustion

The method of exhaustion (methodus exhaustionibus, or méthode des anciens) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape.

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Microwaves are a form of electromagnetic radiation with wavelengths ranging from one meter to one millimeter; with frequencies between and.

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The National Aeronautics and Space Administration (NASA) is an independent agency of the executive branch of the United States federal government responsible for the civilian space program, as well as aeronautics and aerospace research.

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Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

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Newton's reflector

The first reflecting telescope built by Sir Isaac Newton in 1668 is a landmark in the history of telescopes, being the first known successful reflecting telescope.

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Niagara River

The Niagara River is a river that flows north from Lake Erie to Lake Ontario.

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Numerical integration

In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations.

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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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Parabolic antenna

A parabolic antenna is an antenna that uses a parabolic reflector, a curved surface with the cross-sectional shape of a parabola, to direct the radio waves.

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Parabolic microphone

A parabolic microphone is a microphone that uses a parabolic reflector to collect and focus sound waves onto a transducer, in much the same way that a parabolic antenna (e.g., satellite dish) does with radio waves.

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Parabolic partial differential equation

A parabolic partial differential equation is a type of partial differential equation (PDE).

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Parabolic reflector

A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound, or radio waves.

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Parabolic trajectory

In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1.

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Parabolic trough

A parabolic trough is a type of solar thermal collector that is straight in one dimension and curved as a parabola in the other two, lined with a polished metal mirror.

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In geometry, a paraboloid is a quadric surface that has (exactly) one axis of symmetry and no center of symmetry.

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Parallel (geometry)

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

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In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.

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Parametric equation

In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.

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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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Pedal curve

The pedal curve results from the orthogonal projection of a fixed point on the tangent lines of a given curve.

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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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Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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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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Point (geometry)

In modern mathematics, a point refers usually to an element of some set called a space.

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Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

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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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In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

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Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

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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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Quadratic form

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.

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Quadratic function

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree.

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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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Radius of curvature

In differential geometry, the radius of curvature,, is the reciprocal of the curvature.

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Rainbow Bridge (Niagara Falls)

The Niagara Falls International Rainbow Bridge, commonly known as the Rainbow Bridge, is an arch bridge across the Niagara River gorge, and is a world-famous tourist site.

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Rational normal curve

In mathematics, the rational normal curve is a smooth, rational curve of degree in projective n-space.

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Reduced-gravity aircraft

A reduced-gravity aircraft is a type of fixed-wing aircraft that provides brief near-weightless environments for training astronauts, conducting research and making gravity-free movie shots.

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Reflecting telescope

A reflecting telescope (also called a reflector) is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image.

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Reflection (physics)

Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated.

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Reflection symmetry

Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, is symmetry with respect to reflection.

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René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

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Roman Empire

The Roman Empire (Imperium Rōmānum,; Koine and Medieval Greek: Βασιλεία τῶν Ῥωμαίων, tr.) was the post-Roman Republic period of the ancient Roman civilization, characterized by government headed by emperors and large territorial holdings around the Mediterranean Sea in Europe, Africa and Asia.

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Rotating furnace

A rotating furnace is a device for making solid objects which have concave surfaces that are segments of axially symmetrical paraboloids.

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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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Rotational symmetry

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.

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Scaling (geometry)

In Euclidean geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions.

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A shape is the form of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture or material composition.

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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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Simpson's rule

In numerical analysis, Simpson's rule is a method for numerical integration, the numerical approximation of definite integrals.

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Solar cooker

A solar cooker is a device which uses the energy of direct sunlight to heat, cook or pasteurise drink and other food materials.

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Solar energy

Solar energy is radiant light and heat from the Sun that is harnessed using a range of ever-evolving technologies such as solar heating, photovoltaics, solar thermal energy, solar architecture, molten salt power plants and artificial photosynthesis.

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In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid.

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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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Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

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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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Stephen Hawking

Stephen William Hawking (8 January 1942 – 14 March 2018) was an English theoretical physicist, cosmologist, and author, who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge at the time of his death.

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The Sun is the star at the center of the Solar System.

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Suspension bridge

A suspension bridge is a type of bridge in which the deck (the load-bearing portion) is hung below suspension cables on vertical suspenders.

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Synthetic geometry

Synthetic geometry (sometimes referred to as axiomatic or even pure geometry) is the study of geometry without the use of coordinates or formulas.

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Syracuse, Sicily

Syracuse (Siracusa,; Sarausa/Seragusa; Syrācūsae; Συράκουσαι, Syrakousai; Medieval Συρακοῦσαι) is a historic city on the island of Sicily, the capital of the Italian province of Syracuse.

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In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

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A telescope is an optical instrument that aids in the observation of remote objects by collecting electromagnetic radiation (such as visible light).

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The Quadrature of the Parabola

The Quadrature of the Parabola (Τετραγωνισμὸς παραβολῆς) is a treatise on geometry, written by Archimedes in the 3rd century BC.

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Thomas Edison

Thomas Alva Edison (February 11, 1847October 18, 1931) was an American inventor and businessman, who has been described as America's greatest inventor.

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A trajectory or flight path is the path that a massive object in motion follows through space as a function of time.

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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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In geometry, a trisectrix is a curve which can be used to trisect an arbitrary angle with ruler and compass and this curve as an additional tool.

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Twisted cubic

In mathematics, a twisted cubic is a smooth, rational curve C of degree three in projective 3-space P3.

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Two-body problem

In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other.

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United States

The United States of America (USA), commonly known as the United States (U.S.) or America, is a federal republic composed of 50 states, a federal district, five major self-governing territories, and various possessions.

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Universal parabolic constant

The universal parabolic constant is a mathematical constant.

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University of Texas at Austin

The University of Texas at Austin (UT, UT Austin, or Texas) is a public research university and the flagship institution of the University of Texas System.

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Veronese surface

In mathematics, the Veronese surface is an algebraic surface in five-dimensional projective space, and is realized by the Veronese embedding, the embedding of the projective plane given by the complete linear system of conics.

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Vertex (curve)

In the geometry of planar curves, a vertex is a point of where the first derivative of curvature is zero.

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Weightlessness, or an absence of weight, is an absence of stress and strain resulting from externally applied mechanical contact-forces, typically normal forces (from floors, seats, beds, scales, etc.). Counterintuitively, a uniform gravitational field does not by itself cause stress or strain, and a body in free fall in such an environment experiences no g-force acceleration and feels weightless.

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Conic section/Proofs, Derivation of parabolic form, Derivations of Conic Sections, Derivations of conic sections, Lambert's Theorem, Parabola/Proofs, Parabolae, Parabolas, Parabolic Equation, Parabolic curve, Parabolic equation, Parabolic motion, X squared.


[1] https://en.wikipedia.org/wiki/Parabola

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