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# Catenary

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. [1]

99 relations: Acta Eruditorum, Anagram, Anchor, Antoni Gaudí, Arc length, Barcelona, Budapest Keleti railway station, Cartesian coordinate system, Casa Milà, Catenary arch, Catenoid, Cesàro equation, Cf., Chain, Chain fountain, Christiaan Huygens, Compression (physics), Ctesiphon, Curve, David Gregory (mathematician), Davies Gilbert, Differential equation, Differential geometry of curves, Elasticity (physics), Electric charge, Electric field, Electromagnetic metasurface, Envelope (mathematics), Equation, Floating wind turbine, Force, Frenet–Serret formulas, Galileo Galilei, Gaspard-Gustave de Coriolis, Gateway Arch, Geometry, Geometry Center, Gottfried Wilhelm Leibniz, Graph of a function, Hooke's law, Hyperbolic function, Involute, Jacob Bernoulli, Joachim Jungius, Johann Bernoulli, Kiln, Leonhard Euler, Limit (mathematics), List of integrals of irrational functions, Mathematical model, ... Expand index (49 more) »

## Acta Eruditorum

Acta Eruditorum (Latin for "reports/acts of the scholars") was the first scientific journal of the German lands, published from 1682 to 1782.

## Anagram

An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once.

## Anchor

An anchor is a device, normally made of metal, used to connect a vessel to the bed of a body of water to prevent the craft from drifting due to wind or current.

## Antoni Gaudí

Antoni Gaudí i Cornet (25 June 1852 – 10 June 1926) was a Spanish architect from Catalonia.

## Arc length

Determining the length of an irregular arc segment is also called rectification of a curve.

## Barcelona

Barcelona is a city in Spain.

## Budapest Keleti railway station

Budapest Keleti (eastern) railway station (Budapest Keleti pályaudvar) is the main international and inter-city railway terminal in Budapest, Hungary.

## 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.

## Casa Milà

Casa Milà, popularly known as La Pedrera or "The stone quarry", a reference to its unconventional rough-hewn appearance, is a modernist building in Barcelona, Catalonia, Spain.

## Catenary arch

A catenary arch is a type of architectural pointed arch that follows an inverted catenary curve.

## Catenoid

A catenoid is a type of surface in topology, arising by rotating a catenary curve about an axis.

## Cesàro equation

In geometry, the Cesàro equation of a plane curve is an equation relating the curvature (\kappa) at a point of the curve to the arc length (s) from the start of the curve to the given point.

## Cf.

The abbreviation cf. (short for the confer/conferatur, both meaning "compare") is used in writing to refer the reader to other material to make a comparison with the topic being discussed.

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## Chain

A chain is a serial assembly of connected pieces, called links, typically made of metal, with an overall character similar to that of a rope in that it is flexible and curved in compression but linear, rigid, and load-bearing in tension.

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## Chain fountain

The chain fountain phenomenon, also known as the self-siphoning beads or the Mould effect, is a counterintuitive physical phenomenon observed with a chain of beads placed inside a jar, when one end of the chain is yanked from the jar and is allowed to fall to the floor beneath.

## Christiaan Huygens

Christiaan Huygens (Hugenius; 14 April 1629 – 8 July 1695) was a Dutch physicist, mathematician, astronomer and inventor, who is widely regarded as one of the greatest scientists of all time and a major figure in the scientific revolution.

## Compression (physics)

In mechanics, compression is the application of balanced inward ("pushing") forces to different points on a material or structure, that is, forces with no net sum or torque directed so as to reduce its size in one or more directions.

## Ctesiphon

Ctesiphon (Κτησιφῶν; from Parthian or Middle Persian: tyspwn or tysfwn) was an ancient city located on the eastern bank of the Tigris, and about southeast of present-day Baghdad.

## Curve

In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.

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## David Gregory (mathematician)

David Gregory (originally spelt Gregorie) FRS (1661 – 10 October 1708) was a Scottish mathematician and astronomer.

## Davies Gilbert

Davies Gilbert (born Davies Giddy, 6 March 1767 – 24 December 1839) was a Cornish engineer, author, and politician.

## Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

## Differential geometry of curves

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus.

## Elasticity (physics)

In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed.

## Electric charge

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.

## Electric field

An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them.

## Electromagnetic metasurface

An electromagnetic metasurface refers to a kind of artificial sheet material with sub-wavelength thickness.

## 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.

## Equation

In mathematics, an equation is a statement of an equality containing one or more variables.

## Floating wind turbine

A floating wind turbine is an offshore wind turbine mounted on a floating structure that allows the turbine to generate electricity in water depths where fixed-foundation turbines are not feasible.

## Force

In physics, a force is any interaction that, when unopposed, will change the motion of an object.

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## Frenet–Serret formulas

In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a continuous, differentiable curve in three-dimensional Euclidean space ℝ3, or the geometric properties of the curve itself irrespective of any motion.

## 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.

## Gaspard-Gustave de Coriolis

Gaspard-Gustave de Coriolis (21 May 1792 – 19 September 1843) was a French mathematician, mechanical engineer and scientist.

## Gateway Arch

The Gateway Arch is a monument in St. Louis, Missouri, United States.

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

## Geometry Center

The Geometry Center was a mathematics research and education center at the University of Minnesota.

## Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

## 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.

## Hooke's law

Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance.

## Hyperbolic function

In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.

## Involute

In the differential geometry of curves, an involute (also known as evolvent) is a curve obtained from another given curve by one of two methods.

## Jacob Bernoulli

Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.

## Joachim Jungius

Joachim Jungius (22 October 1587 &ndash; 23 September 1657) was a German mathematician, logician and philosopher of sciences.

## Johann Bernoulli

Johann Bernoulli (also known as Jean or John; – 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family.

## Kiln

A kiln (or, originally pronounced "kill", with the "n" silent) is a thermally insulated chamber, a type of oven, that produces temperatures sufficient to complete some process, such as hardening, drying, or chemical changes.

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## Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

## Limit (mathematics)

In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value.

## List of integrals of irrational functions

The following is a list of integrals (antiderivative functions) of irrational functions.

## Mathematical model

A mathematical model is a description of a system using mathematical concepts and language.

## Mechanical equilibrium

In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero.

## Minimal surface

In mathematics, a minimal surface is a surface that locally minimizes its area.

## Minimal surface of revolution

In mathematics, a minimal surface of revolution or minimum surface of revolution is a surface of revolution defined from two points in a half-plane, whose boundary is the axis of revolution of the surface.

## National Historic Landmark

A National Historic Landmark (NHL) is a building, district, object, site, or structure that is officially recognized by the United States government for its outstanding historical significance.

## Nicolas Fuss

Nicolas Fuss (29 January 1755 – 4 January 1826), also known as Nikolai Fuss, was a Swiss mathematician, living most of his life in Imperial Russia.

## Notices of the American Mathematical Society

Notices of the American Mathematical Society is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue.

## Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

## 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.

An overhead line or overhead wire is used to transmit electrical energy to trams, trolleybuses or trains.

## Parabola

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

## Parabolic arch

A parabolic arch is an arch shaped like a parabola.

## Parameter

A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

## Parametric equation

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

## Park Güell

The Park Güell (Parc Güell) is a public park system composed of gardens and architectonic elements located on Carmel Hill, in Barcelona, Catalonia (Spain).

## Physics

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.

## Popular Mechanics

Popular Mechanics is a classic magazine of popular science and technology.

## Position (vector)

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line from O to P. The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.

## Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

## Robert Hooke

Robert Hooke FRS (– 3 March 1703) was an English natural philosopher, architect and polymath.

## Roulette (curve)

In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, and involutes.

## Royal Society

The President, Council and Fellows of the Royal Society of London for Improving Natural Knowledge, commonly known as the Royal Society, is a learned society.

## 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.

## Sheffield Winter Garden

Sheffield Winter Garden in the city of Sheffield in South Yorkshire is one of the largest temperate glasshouses to be built in the UK during the last hundred years, and the largest urban glasshouse anywhere in Europe.

## 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.

## Simple suspension bridge

A simple suspension bridge (also rope bridge, swing bridge (in New Zealand), suspended bridge, hanging bridge and catenary bridge) is a primitive type of bridge that is supported entirely from anchors at either end and has no towers or piers.

## Speed of light

The speed of light in vacuum, commonly denoted, is a universal physical constant important in many areas of physics.

## Spring (device)

A spring is an elastic object that stores mechanical energy.

## Square wheel

A square wheel is a wheel that, instead of being circular, has the shape of a square.

## St Paul's Cathedral

St Paul's Cathedral, London, is an Anglican cathedral, the seat of the Bishop of London and the mother church of the Diocese of London.

St.

## Steel catenary riser

A steel catenary riser (SCR) is a common method of connecting a subsea pipeline to a deepwater floating or fixed oil production platform.

## Stiffness

Stiffness is the rigidity of an object &mdash; the extent to which it resists deformation in response to an applied force.

## Stressed ribbon bridge

A stressed ribbon bridge (also stress-ribbon bridge or catenary bridge) is a tension structure (similar in many ways to a simple suspension bridge).

## Surface area

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

## Surface of revolution

A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) around an axis of rotation.

## 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.

## Tangential angle

In geometry, the tangential angle of a curve in the Cartesian plane, at a specific point, is the angle between the tangent line to the curve at the given point and the -axis.

## Taq Kasra

Tāq Kasrā, also transcribed as Taq-i Kisra, Taq-e Kesra, (طاق کسری) and Ayvān-e Kasrā (ایوانِ کسری); meaning Iwan of Khosrow) are names given to the remains of a ca. 3rd–6th century Sasanian Persian monument, which is sometimes called the Archway of Ctesiphon. It is located near the modern town of Salman Pak, Iraq. It is the only visible remaining structure of the ancient city of Ctesiphon. The archway is considered a landmark in the history of architecture, and is the largest single-span vault of unreinforced brickwork in the world.

## Tension (physics)

In physics, tension may be described as the pulling force transmitted axially by the means of a string, cable, chain, or similar one-dimensional continuous object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements.

## Thomas Jefferson

Thomas Jefferson (April 13, &#91;O.S. April 2&#93; 1743 – July 4, 1826) was an American Founding Father who was the principal author of the Declaration of Independence and later served as the third president of the United States from 1801 to 1809.

## Thomas Paine

Thomas Paine (born Thomas Pain; – In the contemporary record as noted by Conway, Paine's birth date is given as January 29, 1736–37. Common practice was to use a dash or a slash to separate the old-style year from the new-style year. In the old calendar, the new year began on March 25, not January 1. Paine's birth date, therefore, would have been before New Year, 1737. In the new style, his birth date advances by eleven days and his year increases by one to February 9, 1737. The O.S. link gives more detail if needed. – June 8, 1809) was an English-born American political activist, philosopher, political theorist and revolutionary.

## Tractrix

A tractrix (from the Latin verb trahere "pull, drag"; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a tractor (pulling) point that moves at a right angle to the initial line between the object and the puller at an infinitesimal speed.

## 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.

## Troposkein

In physics and geometry, the troposkein is the curve an idealized rope assumes when anchored at its ends and spun around its long axis at a constant angular velocity.

## Two New Sciences

The Discourses and Mathematical Demonstrations Relating to Two New Sciences (Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze), published in 1638 was Galileo's final book and a scientific testament covering much of his work in physics over the preceding thirty years.

## Weight

In science and engineering, the weight of an object is related to the amount of force acting on the object, either due to gravity or to a reaction force that holds it in place.

## Weighted catenary

A weighted catenary is a catenary curve, but of a special form.

## Whewell equation

The Whewell equation of a plane curve is an equation that relates the tangential angle (\varphi) with arclength (s), where the tangential angle is the angle between the tangent to the curve and the x-axis, and the arc length is the distance along the curve from a fixed point.

## Wire rope

Steel wire rope (right hand langs lay) Wire rope is several strands of metal wire twisted into a helix forming a composite "rope", in a pattern known as "laid rope".

## References

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